Ms Kuenssberg said: "Mr President, you've said before that torture works, you've praised Russia, you've said you want to ban some Muslims from coming to America, you've suggested there should be punishment for abortion.
"For many people in Britain those sound like alarming beliefs. What do you say to our viewers at home who are worried about some of your views and worried about you becoming the leader of the free world?"
I guess @bbclaurak speaks for the people of Britain in the same way @lilyallen apologises for the people of Britain. Not in my name
Pointing to Ms Kuenssberg and turning to Theresa May, Mr Trump said: "This was your choice of a question?"
Leaning in to the microphone with a smile, he added: "There goes that relationship."
The grilling prompted laughter in the room but some viewers branded Ms Kuenssberg’s questioning as “rude” and an “embarrassment”.
Controversial commentator Katie Hopkins said: “I guess @bbclaurak speaks for the people of Britain in the same way @lilyallen apologises for the people of Britain. Not in my name.”
AFP GETTY/ SKY
BBC political editor Laura Kuenssberg questioned Donald Trump during a press conference
@vastmajority22 said the BBC political editor had “tarnished the reputation of the BBC in the USA”.
Wendy Hayward tweeted: “I thought the BBC question was rude and I felt embarrassed”.
JL Foxsten said: “The BBC question was an embarrassment and extremely rude. Sounded like a crusading sixth form student.”
@MrBenPen tweeted: “Shame on this reporter, and shame on the BBC. They do not represent the British people. Rude and disrespectful. Pathetic bias!”
Controversial commentator Katie Hopkins weighed in on the incident
@MrBenPen accused Ms Kuenssberg of "pathetic bias"
Donny Brexit branded the incident an “utter embarrassment to the UK"
JL Foxsten said the question was "extremely rude"
@vastmajority22 said the incident “tarnished the reputation of the BBC in the USA”
Wendy Hayward tweeted she was "embarrassed" by the incident
Donny Brexit branded the incident an “utter embarrassment to the UK, liberal lefty bubble question”.
Others praised the journalist for her work.
Natalie McCormack said: “Bloody brilliant! Glad to see someone call him out. Shame our Prime Minister can’t do the same”.
Jane Northedge said: “You’re a star. Show him what it means to have a free press. Thank you”.
Adam Paulson said: “Brave and necessary. Well done.”
Jane Northedge said Ms Kuenssberg was a "star" for her questioning
Natalie McCormack praised Ms Kuenssberg
@joebones40 praised the BBC political editor
Kev Wright said the political editor's question was "superb"
Adam Paulson praised the reporter's work
Journalist Patrick Kidd applauded Ms Kuenssberg’s questioning
@Kev Wright said: “Well done Laura, superb question.”
Patrick Kidd said: “Good for @bbclaurak showing how – albeit very politely – journalists can bring up unwelcome elements of politics in press conferences”.
@joebones40 said: “Well done @bbclaurak superb question……no holds barred, unlike the softballs from the US press.”
Responding to Ms Keunssberg, Mr Trump repeated his belief that torture does work, but said he would leave the final decision to his defence secretary James Mattis.
May meets Trump: Historic first meeting in pictures
Fri, January 27, 2017
The two leaders will spend about an hour in face-to-face talks in the Oval Office, where President Trump has restored a bust of Winston Churchill removed by predecessor Barack Obama.
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President Trump Meets With British PM Theresa May At The White House
On Russia he admitted he does not know the country's president Vladimir Putin well, but he expressed his hope for a "fantastic relationship" between the two nations.
Mr Trump said he could not predict how good a relationship he would have with other countries.
Smiling, he added: "Theresa, we never know about those things, do we?"
He finished by saying: "I will tell you one thing, I will be representing the American people very strongly."