The former First Minister was scolded during the three-hour debate after he claimed he was struggling to hear Foreign Office Minister Sir Alan Duncan.
Mr Salmond stood up as the chairman of the debate intervened.
Thousands of people have gathered outside Westminster Hall in Parliament Square to protest the state visit.
Mr Salmond said: “There are tens of thousands of people protesting outside. I’m having difficulty hearing the minister.”
An angry Sir Alan fumed: “No you’re not!”
SIT DOWN! Alex Salmond was scolded during the Donald Trump debate
That is not eligible. Sit down!
Mr Salmond remained on his feet and as he raised his voice, the chairman of the debate Charles Walker shouted: “That is not eligible. Sit down!”
It comes after the SNP MP branded Theresa May desperate for offering Mr Trump a state visit after his first seven days in office.
Campaigners have called for the visit to be stripped of the trappings of a state occasion in order to avoid causing "embarrassment" to the Queen.
Alex Salmond complains he cannot hear the debate
"Sit down!" Chairman Charles Walker orders Alex Salmond to shut up
The petition said: “Donald Trump should be allowed to enter the UK in his capacity as head of the US Government, but he should not be invited to make an official State Visit because it would cause embarrassment to Her Majesty the Queen.”
More than 1.8million people signed the petition forcing the debate in Westminster Hall today, which could run for three hours.
But the Government insists the US President should meet the Queen.
In a statement, the Foreign Office said: “HM Government believes the President of the United States should be extended the full courtesy of a State Visit. We look forward to welcoming President Trump once dates and arrangements are finalised.
“This invitation reflects the importance of the relationship between the United States of America and the United Kingdom. At this stage, final dates have not yet been agreed for the State Visit.”
A counter-petition calling for Mr Trump to be allowed to make a State Visit received more than 300,000 signatures.
Commons Speaker John Bercow has also become embroiled in the row after effectively banning Mr Trump from addressing MPs and peers during his visit.
It comes as thousands of people protest the planned visit.
What a month for President Trump!
Mon, February 20, 2017
President Donald Trump is making a significant impact on global politics during his first term.
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US President Donald Trump speaks to the press in front of a Boeing 787-10 Dreamliner during its unveiling in North Charleston, South Carolina, on February 17, 2017 .
The Stop Trump coalition has called a nationwide day of action and dozens of protests have been coordinated by the One Day Without Us movement celebrating the contribution of immigrants to British society.
The rally in Parliament Square, which organisers claim will attract more than 20,000 people, was addressed by speakers including joint Green Party leader Caroline Lucas and comic Shappi Khorsandi.
Live updates below from 4.30pm. Refresh this page to see the latest on the Westminster Hall debate.
7.27pm update: Following three hours of heated discussion, those against the state visit win the debate.
But the debate does not have any direct impact on Government decision.
Instead it is just used to apply pressure, but Theresa May is expected to let the state visit go ahead.
7.15pm update: Sir Alan Duncan, Foreign Office minister, shouts down Alex Salmond over claims the protest outside it too loud.
Mr Salmond said: “There are tens of thousands of people protesting outside. I’m having difficulty hearing the minister.”
An angry Sir Alan fumed: “No you’re not!”
Pressing on with the official Government line, Sir Alan says: “This is a special moment for the special relationship.
“The visit should happen, the visit will happen and when it does I trust the UK will extend a polite and generous welcome to President Donald Trump.”
6.55pm update: Tasmina Ahmed-Sheikh condemns Sir Edward Leigh for his earlier defence of Mr Trump’s comments toward women.
The SNP MP says: “The women in this House have had enough of it and we will not put up with it.”
Onto the Royal Family and Mr Trump's comments about photographers making money from photos of the Duchess of Cambridge sunbathing, Miss Ahmed-Sheikh says: "What family would want to welcome that man into their home?"
In 2012, Mr Trump tweeted: “Who wouldn’t take Kate’s picture and make lots of money if she does the nude sunbathing thing. Come on Kate!”
The photos were published in a French magazine with six defendants now facing a criminal trial over the incident.
Nigel Adams, Tory MP for Selby and Ainsty, asks: “I’m a little bit confused. Many members have mentioned unsavoury figures that have been afforded state visits. Are we not slipping into double standards.”
Labour’s Dawn Butler says the US “has a virus”
6.49pm update: Liam Byrne, Labour MP for Birmingham Hodge Hill, says he fears the state visit will “not be a showcase for shared values but for the divisions between us”.
He adds: “What we are going to get is the kind of protest we see outside, what will greet the president will make the protest outside look like a tea party.”
Mr Byrne warns the special relationship will become “strained” if a state visit goes ahead.
The Labour MP adds British Prime Ministers have long overestimated their influence over their American counterparts.
She says: “My best hope is we keep it short, because it will not be sweet.”
The sounds of the protest outside are filtering into Westminster Hall as MPs deliver their closing arguments.
6.44pm update: Labour’s Dawn Butler says the US “has a virus” and Britain must stop a “pandemic”.
She says: “We cannot sell our souls and what we believe in, in order to sell our goods and services.
“It is too high a cost to pay. The antidote to this virus is to build bridges not walls.
“People have come out to march outside Parliament because they believe in hope not hate.”
She urges MPs "not to be on the wrong side of history."
6.41pm update: Gregory Campbell, DUP for East Londonderry, is shouting in Westminster Hall.
He says: “I do not endorse some of the things he has said, but he has been invited and we should honour that.”
6.35pm update: Alistair Carmichael, Lib Dem for Orkney and Shetland, says: “This is week one of a four year termed what having offered a state visit this time are we going to offer the next time we want to get a favourable response. Will it be the crown jewels? Anything is possible these days.
“This is a question of judgement and in my view the PM got it catastrophically wrong. What was the motivation for this? My personal suspicion is she was a little spooked of seeing Nigel Farage in Trump Tower or maybe trying to pursue trade deals post-Brexit. Whatever the motivation, it has made us look desperate.”
6.23pm update: Anne Main, Tory MP for St Albans, says MPs in favour of the visit are not apologists for the US president’s behaviour.
She says: “It’s the old adage, when arguing with a prostitute about the price and she says, when he’s offering her tuppence, ‘what do you take me for’, and he said ‘I think we know’.
“This is now our negotiating strategy.
“Oh let’s have some fake outrage here, I think everybody’s heard this comment before.
“I’m standing here as a woman being shouted down by women”.
6.17pm update: As protests rage against Donald Trump in Parliament Square, SNP MP Roger Mullin says this is a “grubby and despicable manoeuvre by this Prime Minister.”
Mark Field: Of course Trump should have state dinner
Sadiq Khan brands Trump's travel ban as 'cruel and shameful'
Donald Trump sparks confusion over 'problems' in Sweden
Alistair Carmichael asks: "What next, the crown jewels?"
6.10pm update: Martin Vickers, Tory MP for Cleethorpes, speaks out in favour of the visit.
He says a state visit for the US president “is in the national interest”.
Mr Vickers adds: “We are rolling out the red carpet for the president, we are not rolling out the red caret for Mr Trump, we are rolling out the red carpet for our most valued ally.”
6.03pm update: Tulip Siddiq, Labour MP for Hampstead and Kilburn, condemns plans for a royal visit.
She warns MPs to stop Mr Trump "spreading hatred"
Miss Siddiq said: “This debate is about the nature of this Government’s response to Donald Trump and whether we give him a royal welcome.
“This man has already made people in this country question if they are still welcome in America.
“What has he said and done and what has he said to the PM to warrant this state visit. In my opinion a state visit should be granted, not expected.
“This does not happen because you have been in position for seven days.”
5.58pm update: Sir Edward Leigh, Tory MP for Gainsborough, has faced an angry backlash for his defence of the state visit.
Sir Edward said the comments were "horrible and ridiculous" but that many politicians will have made "some ridiculous sexual comment" in private.
He said: "It is very foolish of us to lecture our conservative colleagues on the other side of the Atlantic about what is the right or the improper nature of conservatism.
"Mr Trump is not my sort of conservative, I really have nothing in common with him, but I will say that let's just look at some of his comments.
"The charge of misogyny – I mean of course what he is reported to have said in a private conversation is absolutely horrible and ridiculous and I hope none of us would make it.
"But which one of us has not made some ridiculous sexual comment some time in our past?"
The remarks were met with groans of outrage by several MPs in Westminster Hall for the debate.
Sir Edward said: "Well, in private? Let he who is without sin cast the first stone, alright? He's apologised, it's not really a reason to withdraw."
Hannah Bardell, SNP MP for Livingston, intervened to express her outrage at the comments.
She said: "I cast no aspersions, but is he seriously suggesting that it is a legitimate perspective and point of view that the comments made, in public, by Trump on a number of issues, including marriage equality for LGBT people, and in private, which were recorded and broadcast, on sexual abuse and attacking women, are a legitimate position?
"And he stands there and thinks it's acceptable to say in this chamber and say in this House that that kind of position is acceptable?"
Defending himself, Sir Edward replied: "I said actually precisely the opposite. As far as I know I've never spoken like that and no friends of mine have ever spoken like that – I completely deplore it and find it ridiculous to speak like that in private.
"All I'm saying is most of us would be rather embarrassed if everything that we said in private in our past was broadcast."
Mr Trump's comments, made in 2005 to a television host and caught on camera, surfaced towards the end of the election campaign and threatened to derail his bid for the White House.
Sir Edward stressed: "He is elected, we have to work with him, which is why it would be a disaster if this invitation was rescinded."
5.51pm update: Kirsten Oswald, SNP MP for East Renfrewshire, says “no wonder there are concerns. What on earth have we come to that the UK Government thought it was a good idea to reward Mr Trump’s behaviour with a state visit.”
She adds Britain should challenge Mr Trump and says his presidency has been defined by “racism and prejudice”.
Miss Oswald says the PM will “take any friend she can get” in her push for a hard Brexit and says the Government has "lost its moral backbone" by allowing Mr Trump to "foster Islamophobia and racism".
Sir Edward Leigh sparked outrage as he defended the state visit
Anne Main says MPs in favour of a Trump state visit are "not apologists" for his behaviour
5.41pm update: An hour into the debate and Naz Shah, Labour MP for Bradford West, delivers a powerful speech criticising Mr Trump’s attitudes to Muslims.
She warns: “We are already on step three three towards genocide. What are we doing allowing Mr Trump to say Muslims are the enemy within.
"That is me as a Muslim in this House. I am not an enemy to Western democracy, I’m part of Western democracy.
"By allowing Donald Trump a state visit what we are doing is endorsing his views that I fought hard against and saying it is ok. I thank the millions who have signed the petition and I really hope we do not honour this president.”
She says: “His rhetoric has been so broad that even I personally as a Muslim feel attacked and misrepresented.
“We have to take every opportunity to show his negativity and divisive messages are not going to divide us.”
Tulip Siddiq condemns the visit
Labour MP Naz Shah says as a Muslim she feels "personally attacked" by Donald Trump
5.36pm update: Labour's Rushanara Ali says MPs defending Mr Trump need to speak out against his “dangerous rhetoric” and “address the issue instead of being apologists for his hatred.”
James Berry, Tory MP for Kingston, says he accepts Miss Ali’s challenge and condemns Mr Trump.
He says: “His attitude to Muslims is an outrage and it is lacking in evidence.”
Miss Ali says: “It is deeply saddening and shameful that colleagues who are defending this visit are not recognising the serious concern that people have, particularly Muslims, but many others, about the dangers of Donald Trump.
"And it's time they spoke out against that kind of hostility, it is deeply divisive and it's time they addressed this issue instead of making excuses and being apologists for his hatred."
5.30pm update: Simon Burns, Tory MP for Chelmsford, campaigned for Hillary Clinton during the election.
He says: “Regardless of what we think of Donald Trump as a man I believe it is in our national interest that we continue to be a candid friend to the United States.
“A candid friend who has the respect of the US and has the ability to speak to them when we believe they are doing it wrong or could be doing it better or so we can ensure they moderate their views in the correct and dignified way to behave.
“We cannot do that if we ignore the presidency straight off the bat. We would become isolated, we would become less influential and it would not be in the national interest.
“I don’t think it matters when one issues an invitation if one is trying to protect the national interest.”
Mr Burns warns we will have to “wait and see” if Mr Trump’s advisors can “moderate and guide him”.
The Tory MP stresses "Britain cannot afford to be isolated" in the wake of Brexit but adds he is not in favour of Mr Trump addressing MPs in Parliament.
Clinton supporter Simon Burns says the state visit should go ahead "in the national interest"
5.24pm update: Jim Cunningham, Labour MP for Coventry South, says: “Donald Trump does not appear to share our values. We should have waited for two years at least before issuing an invitation.”
5.22pm update: Stephen Doughty, Labour and Co-operative MP, says: “I believe we should have contact with any American administration.”
Mr Doughty adds he was “disappointed” that George W Bush’s administration led to feelings of anger towards Americans.
He says he is “deeply frightened and deeply concerned” that the US constitution has been “attacked” by Mr Trump.
The Labour MP says it is right for Mrs May to meet with Mr Trump but says "we choose how we engage on these issues". Praises Canadian PM Justin Trudeau for "maintaining his integrity" when dealing with the White House.
Mr Doughty accuses the PM of "rushing into offering the champagne, the glamour, the red carpet…giving it all up on a plate in one week".
5.20pm update: Tory MP James Cartlidge says he would offer a state visit to Vladimir Putin.
He warns: “There will be smiles all round in the Kremlin if we follow this petition.”
Mr Cartlidge stresses Moscow wants to “divide the West”.
He adds: “Our foreign policy is about the national interest of the UK.
“I would offer a state visit to Vladimir Putin as was done by Tony Blair. That’s despite the fact Russian Bear bombers are buzzing our airspace, that they have nuclear missiles pointed at us, that they pose this huge threat.
“That’s precisely why we do it, because we want to influence the administration.”
5.15pm update: Mr Salmond warns MPs not to underestimate Mr Trump and says Britain must be careful when negotiating with the Republican.
The former First Minister urges the Government to rescind the state visit invite before “any more embarrassment” is caused.
Mr Salmond said: "As an example of fawning subservience… the Prime Minister's holding hands across the ocean visit would be difficult to match.
"To do it in the name of shared values was stomach churning.
"What exactly are the shared values that this House, this country, would hope to have with President Trump?"
He says the US president is "not a stupid man", adding it is a "recipe for total and utter disaster" for the UK to advertise its weak position to Mr Trump.
"From my experience of negotiating with Donald Trump, let me tell the honourable member, never ever do it from a weak position because the result will be total disaster."
5.12pm update: Rushanara Ali, Labour MP for Bethnal Green, says a state visit would damage the monarchy.
She says: “Given President Trump’s remarks about torture, his misogynistic stance against women and Muslims, affording him a state visit does huge amounts of damage to our Queen and monarchy.”
5.09pm update: Julian Lewis, Tory MP and Chair of Commons Defence Committee, says the debate should go further than discussing the “personal qualities of any individual”.
Mr Trump has cast doubt on the future of US contributions to NATO.
He says NATO is “our best guarantee of World War Three not breaking out in the 21st century.”
“Do you really think it is more important to berate him, castigate him and encourage him to retreat into some sort of bunker?”
He defends Theresa May, who was photographed holding the Republican’s head during her White House visit.
Mr Lewis says she was right to “take him by the hand and try to lead him down the path of righteousness”.
Tory MP Julian Lewis defends Theresa May for "taking Mr Trump by the hand"
4.57pm update: David Lammy, Labour MP for Tottenham, also queries the speed of the state visit invite. Says he is a great friend of the US but says the "contentious election" should afford Mr Trump an official visit, but no meeting with the Queen.
Mr Lammy adds he is concerned about Mr Trump's comments towards women and behaviour toward Hillary Clinton.
He adds: “I think of my five year old daughter when I think about a man who thinks it’s okay to go and grab p***.
“I think about a man who thinks it’s ok to be so misogynistic towards the woman he’s running against.
“And frankly I can’t imagine a leader of our own country of whatever political stripe behaving in that manner.”
He says: "We didn't do this for Kennedy, we didn't do this for Truman, we didn't do this for Reagan. But for this man after seven days we say we will do all this because we are so desperate for his company.
"I'm ashamed it has come to this. We should think very carefully about a president whose attitude towards the press is abhorrent, we should think about a president who has put so many people in fear. For that reason we should not afford him a state visit."
He asks why Britain would "abandon all its principles" to invite Mr Trump "because this country is so desperate for a trade deal that we would throw all our own history out the window?”
David Lammy says Mr Trump should only be given an official visit
Mr Evans condemns "the trolling of Melania and Barron Trump"
4.53pm update: Mr Evans says "we are attacking the 61million American people who voted for Mr Trump" when Britons accuse the US president of racism.
Mr Evans, Tory MP for Ribble Valley, says: “We have to ask ourselves why is it that people felt so left behind that they made the democratic decisions they have that some of us can’t understand. The fact is, the people have. These were the forgotten people.
"They are the ones who packed that stadium on Saturday to cheer Donald Trump after his first month. They like what he says. We may not like some of the things he says but I do respect he has stood on a platform that he is now delivering. He is going to go down in history for being condemned for delivering on his promises.”
He calls for his fellow MPs to "condemn the trolling of Melania and Barron Trump". Mr Trump's wife and youngest son have been subject to online abuse in recent weeks.
Mr Evans stresses "the people who have been left behind have spoken".
Mr Evans is heckled for his defence of Mr Trump’s right to visit Britain.
He accuses MPs of “double standards” for not trying to ban China’s premier Xi Jinping from making a state visit.
The UK Protests Against President Trump
Mon, February 20, 2017
President Trump signed an executive order banning immigration to the USA from seven 'muslim' countries. This led to protests across America and, now, the UK.
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A demonstrator holds a banner that reads
A furious Mr Evans says: “Where were the demonstrations then?
“We had a state visit from a Chinese leader 10 years after Tiananmen Square!”
4.48pm update: Mr Flynn claims the Queen would find the state visit “difficult”.
Chairman Charles Walker tells off Tory MP Nigel Evans for challenging Mr Flynn.
Mr Walker says: “We are not dragging the monarch into this debate, alright colleagues?”
4.45pm update: Green MP Caroline Lucas blasts Mr Trump’s “contempt for basic climate science”.
Her Brighton constituency had the most supporters for the petition against the state visit.
Mr Flynn replies: “It’s extraordinary that Trump from the cavernous depths of his scientific ignorance is prepared to challenge the conclusions of 97% of the world experts on this matter.
“It’s a bad science, conspiracy theory conclusions that he makes.”
Paul Flynn calls the invitation "unprecedented"
Alex Salmond says the speedy invitation is "desperate"
4.40pm update: Onto Mr Trump's infamous comments about women which were leaked during the campaign trail.
Labour's Paula Sheriff says: "Does Mr Flynn agree that to use the expression 'grab them by the ****' to desribe a sexual assault suggest he should not be afforded a visit by the Queen?"
Mr Flynn says he "entirely agrees" and says "his manner and behaviour throughout the election period is one that is greatly worrying".
4.35pm update: The SNP's Alex Salmond says the speedy invitation "stinks of desperation for a trade deal".
Mr Flynn sticks the boot into the Prime Minister after she said she could be a "bridge builder" between the US and Britain. He adds there is no need for a bridge thanks to "Mr Trump's incessant tweets".
Tory Mark Pritchard says: "The special relationship between the US and Britain goes beyond any president at any one time."
Mr Flynn says: "There is no question of disrespect towards the US but there is tremendous concern…Mr Trump has caused problems with every area he has become involved in."
No precedence for State Visit invitation so soon after election. PM in spluttering undignified haste to fawn over worst ever US President.
— Paul Flynn (@PaulFlynnMP) February 7, 2017
4.30pm update: Paul Flynn, MP for Newport West, will open the debate. The Labour MP has criticised the visit, saying there is “no precedence for a state visit inauguration so soon after election.”
Barack Obama received an invitation after 758 days, while it took 978 days before his predecessor, George W. Bush, was offered a state visit, compared with seven days for Mr Trump.
Mr Flynn tweeted: “No precedence for State Visit invitation so soon after election. PM in spluttering undignified haste to fawn over worst ever US President.”
Opening the debate, Mr Flynn said: "One petition says he should not be accorded the rare privilege of a state visit. Only two US presidents have been granted that extraordinary privilege since 1992."
He branded Mrs May's invitation "unprecedented".