London (AFP) - Britain was reeling Thursday after US President Donald Trump castigated Prime Minister Theresa May over her rebuke to him for posting anti-Muslim tweets, but the government sought to play down the row.

Plunging headlong into a high-profile spat with one of America's closest international partners, Trump suggested May focus on defending Britain rather than criticising him after he retweeted anti-Muslim videos from a British far-right group.

"@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!" Trump tweeted late Wednesday.

Trump had to delete an earlier tweet with the same message after he used the wrong Twitter handle for May, instead tagging @theresamay, who is reportedly a 41-year-old mother from Bognor Regis with just six followers.

There were calls for Trump's planned state visit to Britain, which has been highly controversial ever since May extended the invitation at her first meeting with him at the White House in January, to be cancelled.

- 'Betrayal of special relationship' -

London Mayor Sadiq Khan, who has been involved in a series of spats with Trump, said it was "increasingly clear that any official visit at all from President Trump to Britain would not be welcomed".

He said Trump's actions were "a betrayal of the special relationship between our two countries".

"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."

Trump drew fierce condemnation at home and abroad for retweeting three incendiary anti-Muslim videos posted by Jayda Fransen, deputy head of the British far-right group Britain First, who has been convicted of a hate crime.

- Trump was 'wrong' -

May said through a spokesman that Trump was "wrong" to promote the "hateful narratives" of the group.

Story continues

Local Government Minister Sajid Javid said Trump had "endorsed the views of a vile, hate-filled racist organisation that hates me and people like me. He is wrong and I refuse to let it go and say nothing."

But the immediate response from the government after Trump's rebuke appeared muted.

"In the end, our relationship with the United States has a longevity to it that will succeed long after presidents come and go," Education Secretary Justine Greening said.

"This is a president that behaves unlike any other in the nature of the tweets he puts out. I don't believe that should be able to undermine an overall important relationship with our country," she said on BBC Radio.

Ann Coulter, a right-wing US commentator who is followed by Trump on Twitter and may have inspired his retweets, defended him in an interview with BBC radio.

"I think he has only given as good as he gets. I think he has been verbally attacked from the mother country for a lot longer than he has been attacking Britain."

Coulter said she had not researched Fransen's background before retweeting.

"People retweeting videos are not researching the bios of the people who sent the video," she said.

Trump's interventions in British politics have strained the so-called "special relationship".

He has infuriated British authorities with his tweets on terrorism in Britain.

Before Trump's latest missive, the White House had scrambled to limit the fallout, saying that even if the anti-Muslim videos were misleading, the president was pointing out a real problem.

"The threat is real, and that's what the president is talking about," said White House spokeswoman Sarah Sanders.

- 'Facts do matter' -

One of the videos falsely claims to show a Muslim migrant beating up a Dutch boy on crutches.

The Dutch embassy in Washington took the unusual step of publicly criticising a sitting US president on Twitter.

"@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."

Another video is described as showing an Islamist mob pushing a teenager off a rooftop, without any context -- it appears to be footage filmed during unrest in Egypt in 2013. A man was executed for his role in the teen's death.

The third video allegedly depicts a Muslim smashing a statue of the Virgin Mary.

Britain First hailed Trump for his support.

The group was formed in 2011 and is known for picketing outside mosques. It has run and lost in several British and European parliament elections.