Controversy erupted on Monday after the Speaker declared he would “strongly oppose” an address from the US President when he comes to the UK on a state visit later this year.
During his speech in the House of Commons, Mr Bercow said: “I would not wish to issue an invitation to President Trump to speak in the Royal Gallery.
“We value our relationship with the United States, if a state visit takes place, that is way beyond and above of the pay grade of the Speaker.
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“However, as far as this place is concerned I feel very strongly that our opposition to racism and to sexism, and our support for equality before the law and an independent judiciary are hugely important considerations.”
Mr Bercow has been heavily criticised for the damning remakes about the US President, however, Mr Salmond defended the outspoken Commons Speaker.
Mr Salmond insisted that Theresa May was the one causing damage to the US-UK relationship as she was negotiating from a "position of weakness".
Speaking to LBC, Mr Salmond said: "I'm speaking as someone who beat Donald Trump in court three times.
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What damaged the relationship is the Prime Minister's behaviour
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"What damages the relationship between Britain and America – and America is not Donald J Trump – what damaged the relationship is the Prime Minister's behaviour in her rush for 'hands across the ocean' in the White House, relationship with Donald Trump.
"It's wrong for two reasons. One it's the wrong thing to do, to ingratiate yourself without taking the time and effort to see how things go.
“And secondly… I can tell you from absolute personal experience, you should never negotiate with Donald Trump from a position of weakness."
The pro-EU politician’s defence of Mr Bercow came after his House of Lords equivalent revealed he had apologised for his critique of Donald Trump.
Lord Fowler said: "[John Bercow] contacted me this morning, he told me that while he maintained his view on the issue, he was genuinely sorry for failing to contact me.
John Bercow has faced calls for his resignation after his comments about Donald Trump
"My view is that I maintain an open mind and consider any request from Mr Trump to address Parliament if and when it is made.
"I do not intend to argue the case for or against Mr Trump’s visit – that is not my role as Speaker."
Mr Bercow has also faced calls for his resignation as Tory MP John Duddridge drafted a question to the Prime Minister, asking for her to allow ministers to unseat the outspoken Speaker.
Mr Duddrige told The Huffington Post: "The Speaker has lost the confidence of the House. He overstepped the mark.
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“He is not there to put forward his views when he starts doing that he becomes incapable of representing the full opinions of the House of Commons.”
However, the Speaker has defended his remarks saying: "The House has always understood that the chair has a role in these matters.
“I was honestly and honourably seeking to discharge my responsibilities to the House.”
Mr Bercow’s remarks about Mr Trump came after a petition to withdraw the Republican President’s invitation reached more than 1.8 million signatures.
Mrs May is expected to uphold the invitation, with reports on Thursday suggesting Mr Trump could travel to Britain in June.
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