US President Donald Trump has sparked outrage in Britain for a sharp rebuke of Prime Minister Theresa May on Twitter after she criticised him for retweeting British far-right anti-Islam videos.

As British politicians lined up Thursday night (AEST) to condemn Mr Trump for sharing videos originally posted by a leader of a British far-right fringe group, the President replied with an unrepentant message.

“Theresa @theresamay, 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,” he tweeted.

His truculent response caused anger in Britain, where there have been several major Islamist militant attacks this year, with one minister describing Mr Trump’s tweets as “alarming and despairing”.

London’s Muslim mayor Sadiq Khan called for the withdrawal of an invitation to the President to make a state visit to Britain.

President Trump has used Twitter to promote a vile, extremist group that exists solely to sow division and hatred in our country. It's increasingly clear that any official visit from President Trump to Britain would not be welcomed. pic.twitter.com/oZ1Kt0JCfY

— Sadiq Khan (@SadiqKhan) November 30, 2017

Ms May, on a visit to Jordan, repeated her view, expressed earlier by her spokesman, that the US leader was wrong for sharing anti-Muslim videos posted by Jayda Fransen, deputy leader of Britain First. But she did not directly respond to Mr Trump’s Twitter rebuke.

“I’m very clear that retweeting from Britain First was the wrong thing to do,” Ms May told reporters in Jordan.

She described the group as a “hateful organisation” that sought to spread division and mistrust.

“The fact that we work together does not mean that we’re afraid to say when we think the United States has got it wrong, and be very clear with them,” May said. She added that Britain had a long-term, enduring relationship with the US.

The British ambassador to the US, Kim Darroch, said he had raised concerns with White House officials.

“British people overwhelmingly reject the prejudiced rhetoric of the far right, which seek to divide communities & erode decency, tolerance & respect,” he wrote on Twitter.

Fransen, who was convicted this month of abusing a Muslim woman and whose group wants to ban Islam, is facing further criminal charges of racially aggravated harassment.

Mr Trump initially addressed his rebuke to a Twitter handle that was not Ms May’s, although he later retweeted to the British leader’s correct account.

British MPs held an urgent session to discuss Trump’s tweets, with parliamentarians from across the political divide united in condemnation.

“By sharing it (the videos), he is either a racist, incompetent or unthinking, or all three,” opposition Labour MP Stephen Doughty said.

Britain’s Middle East minister Alistair Burt tweeted: “The White House tweets are both alarming and despairing tonight. This is so not where the world needs to go.”

As Minister for the Middle East, proud of our relationships with the Islamic world and those within it, the White House tweets are both alarming and despairing tonight. This is so not where the world needs to go.

— Rt Hon Alistair Burt (@AlistairBurtUK) November 29, 2017

In a thinly veiled reference to Mr Trump, the top UN human rights official on Thursday condemned “populists” who spread “hatred through tweets”.