The London Mayor Sadiq Khan said the action was a "betrayal"
The British Prime Minister Theresa May has launched her first direct condemnation of US President Donald Trump, saying she is "very clear that re-tweeting from Britain First was the wrong thing to do".
Speaking on a trip to Jordan, she replied to President Trump's public challenge made overnight on Twitter.
She told reporters: "The fact that we work together, does not mean that we're afraid to say when we think the United States have got it wrong.
"I am very clear that retweeting Britain First was the wrong thing to do."
Mrs May added: "I'm not a prolific tweeter myself, and that means I don't spend much of my time reading other people's tweets.
"But when I feel there should be a response, I give it - and I've given it."
Her comments are the first direct challenge made to President Trump since a Downing Street statement on Wednesday.
It called the sharing of anti-Muslim videos from a far-right party "wrong".
But the move angered the US leader, who tweeted: "@Theresa_May, 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!"
.@Theresa_May, 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!— Donald J. Trump (@realDonaldTrump) November 30, 2017
This was after an earlier tweet, which tagged the wrong Theresa May on Twitter, was deleted.
At a press conference in Amman, Jordan, Mrs May reiterated the criticism made by British Home Secretary Amber Rudd that the original posts were "wrong".
But she dodged questions on whether President Trump was "a fit person to meet the Queen" on a planned state visit to Britain.
And she avoided answering on whether she would sack a Cabinet minister if they re-tweeted Britain First material, saying only that she was sure they would not.
Earlier, Mrs Rudd said "many of us" shared the view President Trump should delete his Twitter account and but impressed the US-UK relationship was "vital".
The Mayor of London Sadiq Khan also denounced Mr Trump's posts as a "betrayal of the special relationship".
He said: "It beggars belief that the President of our closest ally doesn't see that his support of this extremist group actively undermines the values of tolerance and diversity that makes Britain so great."
Mr Khan, who was targeted directly by the US president for his response to the London Bridge terror attack, added his most recent intervention should see a planned state visit cancelled.
He said: "As the mayor of this great diverse city, I have previously called on Theresa May to cancel her ill-judged offer of a state visit to President Trump.
"After this latest incident, it is increasingly clear that any official visit at all from President Trump to Britain would not be welcomed.
"The Prime Minister of our country should be using any influence she and her government claim to have with the president and his administration to ask him to delete these tweets and to apologise to the British people."
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
Mr Trump retweeted the posts to his 43.6 million followers, including unverified footage purporting to show Muslims committing crimes.
One of the videos claimed to show a Muslim migrant attacking a Dutch boy, but the claim was quickly debunked by Dutch officials:
.@realDonaldTrump Facts do matter. The perpetrator of the violent act in this video was born and raised in the Netherlands. He received and completed his sentence under Dutch law.— Netherlands Embassy 🇺🇸 (@NLintheUSA) November 29, 2017
US Senator Bernie Sanders said: "I don't make it a habit to respond to every ugly tweet from President Trump. If I did, I’d have little time for anything else. But even for Trump, today's retweets of a series of offensive videos from a British right-wing, anti-Muslim fringe group reaches a new low.
"I know that Trump is not much into history or the US Constitution, but he ought to know that millions of men and women have struggled, fought and died to defend our democracy and the religious freedom that our Constitution guarantees."
The Council on American-Islamic Relations (CAIR) described the retweets as an "incitement to violence against American Muslims".
It executive director Nihad Awad argued: "President Trump’s actions are putting the lives and safety of American Muslim children and families at risk.
"Hate speech leads to hate crimes. When hate speech and conspiracy theories against American minorities go unchallenged, they foster an atmosphere that causes hate crimes."
Britain First's Jayda Fransen (31) has faced a number of legal issues. Last year she was found guilty of religiously aggravated harassment "after hurling abuse at a Muslim woman wearing a hijab", The Guardian reports.
Additional reporting: Jack Quann and IRN