There are growing calls for the May government to rescind its invitation to Trump for an official state visit to Britain, which would involve a possible street parade and visit to meet the Queen.

But Prime Minister Theresa May said on Thursday the invitation still stands, though a date is yet to be agreed.

Kim Darroch, Britain's ambassador to Washington, said he had "raised concerns" with the White House on Wednesday in response to Trump retweeting three videos posted by Britain First.

"British people overwhelmingly reject the prejudiced rhetoric of the far right, which seek to divide communities & erode decency, tolerance & respect," he tweeted.

British Home Secretary Amber Rudd, responsible for anti-terrorism operations on British soil, implied on Thursday that she thought Trump should delete his Twitter account.

The House of Commons called an emergency debate on Thursday after Trump doubled down on his three retweets of anti-Muslim posts by Jayda Fransen, the deputy leader of the far-right fringe party Britain First.

Fransen, 31, is facing hate speech charges over a speech she delivered in Northern Ireland in August. In 2016 she was fined ??2000 ($3500) after being found guilty of religiously aggravated harassment for hurling abuse at a Muslim woman wearing a hijab, telling her Muslim men were "coming into my country raping women across the continent".

Trump retweeted three videos tweeted by Fransen, one purporting to be of an atrocity by Islamic extremists, a second the destruction of a statue of the Virgin Mary, and the third an attack on a Dutch teenager on crutches, allegedly by Muslim immigrants. The third video has been discredited by Dutch authorities who said both boys were Dutch.

The retweets by Trump appear to have added 26,000 followers to Fransen's Twitter account - a 50 per cent increase on two days ago - and she publicly thanked him. On Wednesday, the group changed its Facebook cover photo to a picture of Trump.

May's official spokesman said it was wrong of Trump to have retweeted Fransen, saying the "prejudiced rhetoric of the far right" was antithetical to British values of decency and tolerance.

But overnight an unapologetic Trump hit back, tweeting directly to May's official Twitter account saying "don't focus on me, focus on the destructive Radical Islamic Terrorism that is taking place within the United Kingdom. We are doing just fine!"

The President originally addressed the tweet to a different Theresa May on Twitter, then retweeted to her correct account.

May, who was on a trip to the Middle East, said on Thursday that retweeting from Britain First "was the wrong thing to do", but did not say she would cancel Trump's state visit.

The Commons debate was called by Labour MP Stephen Doughty, who said Trump was "either a racist, incompetent or unthinking - or all three" for sharing the videos.

In response, Home Secretary Rudd told Parliament "we have been clear [that] President Donald Trump was wrong to retweet videos hosted by the far right group, Britain First".

But she said her government also looked at "the wider picture, the relationship between the UK and America".

"I know how valuable the friendship is between our two nations," she said. "As Home Secretary, I can tell the House that the importance of the relationship between our countries - the unparalleled sharing of intelligence between our countries - is vital. It has undoubtedly saved British lives. That is the bigger picture here and I urge people to remember that."

Conservative Peter Bone asked: "Would not the world be a better place if the Prime Minister could persuade the President of the United States to delete his Twitter account?"

In response, Rudd said: "I am sure that many of us share [this] view".

Many other politicians were highly critical of Trump.

Sajid Javid, secretary of state for communities and local government, said Trump had "endorsed the views of a vile, hate-filled racist organisation that hates me and people like me".

Fellow Conservative George Freeman called it a "sad and low moment" in Anglo-American relations that "betrays a deep ignorance", and former Blair transport secretary, now Lord Andrew Adonis said he could not think of a more insulting or destructive public communication from a US president to a British PM in recent history.

Liberal Democrat leader Vince Cable called on May to rescind Trump's invitation to a state visit, saying she must "end [the] humiliating dependence of Brexit Britain on [the] goodwill of [an] evil racist".

Veteran Labour MP Dennis Skinner called Trump a "fascist president".

Labour's shadow foreign secretary Emily Thornberry said Trump's tweets put the Queen in a "very difficult and invidious position" if she had to host him next year", a year "which is supposed to be a really happy year for the royal family".

She said Trump "certainly shouldn't come next year", and should postpone his visit "until the British people love him".

"One of my colleagues was murdered by someone shouting 'Britain first'," she said, referring to the murder of Labour MP Jo Cox by a right-wing extremist in 2016.

"You cannot be friends with this man and his values are not ours," Thornberry said.

London mayor Sadiq Khan, who has clashed with Trump before on social media and has previously called for May to cancel her "ill-judged" offer of a state visit to Trump, said "after this latest incident it is increasingly clear that any official visit at all from President Trump to Britain would not be welcomed", and he said May should ask Trump to delete his tweets.