US President Donald Trump has fired back at British Prime Minister Theresa May over her criticism of his retweeting of anti-Muslim videos, saying she should focus on terrorism in Britain.

The only problem was that the Twitter handle Mr Trump included in his tweet did not belong to the British leader, which is @theresa_may and is verified with a blue tick.

Instead he sent the missive to @theresamay, which belongs to an account under the name of Theresa Scrivener, who has six followers and nine tweets.

"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," Trump tweeted.

He corrected the tweet and sent it to the right person shortly afterwards.

.@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

Britain criticised Mr Trump after he retweeted anti-Islam videos originally posted by a leader of a far-right British fringe party who was convicted earlier this month of abusing a Muslim woman.

The White House defended Trump's retweeting of the videos, as criticism poured in from US-based Muslim advocacy groups and the Anti-Defamation League.

Jayda Fransen, deputy leader of the anti-immigration Britain First group, posted the videos which she said showed a group of people who were Muslims beating a teenage boy to death, battering a boy on crutches and destroying a Christian statue.

Mr Trump's decision to retweet the videos prompted criticism from both sides of the Atlantic, with some British lawmakers demanding an apology and US Muslim groups saying it was incendiary and reckless.

AAP

"It is wrong for the president to have done this," the spokesman for British Prime Minister Theresa May said.

"Britain First seeks to divide communities through their use of hateful narratives which peddle lies and stoke tensions. They cause anxiety to law-abiding people."

Reuters was unable to immediately verify the videos and Fransen herself said they had come from various online sources which had been posted on her social media pages.

"I'm delighted," Fransen, who has 53,000 Twitter followers, told Reuters, saying it showed the US president shared her aim of raising awareness of "issues such as Islam".

"Look, I'm not talking about the nature of the video," White House spokeswoman Sarah Sanders told reporters.

"The threat is real and that's what the president is talking about is the need for national security, the need for military spending, and those are very real things. There's nothing fake about that."

David Duke, a former Ku Klux Klan leader, praised Trump. "He's condemned for showing us what the fake news media won't," Duke wrote on Twitter. "Thank God for Trump! That's why we love him!"