US President Donald Trump has hit out at British Prime Minister Theresa May after she said he was wrong to retweet videos posted by a leader of British far-right group Britain First.

"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!", the President tweeted this morning.

The President used the wrong Twitter handle for the British PM, issuing an amended tweet with the correct handle — @theresa_may — about 20 minutes later.

Late yesterday Mr Trump retweeted three videos from fringe group Britain First, sparking outrage in the UK and the rebuke from Number 10 Downing Street.

The videos were originally posted by Britain First deputy leader Jayda Fransen, who said they showed a group of people who were Muslims beating a teenage boy to death, battering a boy on crutches and destroying a Christian statue.

One of the videos, titled "Muslim migrant beats up Dutch boy on crutches!", has been discredited by the Netherlands embassy in the United States.

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Ms May's spokesman, James Slack, said it was "wrong" for the President to have retweeted Britain First, as the group sought to divide communities through its use of "hateful narratives which peddle lies and stoke tensions".

The retweets also drew criticism from British Foreign Minister Boris Johnson, who said on Twitter that "hate speech has no place" in the UK.

The White House defended the tweets, saying Mr Trump shared them to start a conversation about immigration.

"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."

During the 2016 US election campaign, Mr Trump called for "a total and complete shutdown of Muslims entering the United States", saying he was raising security issues.

As President, he has issued executive orders banning entry to some citizens of several Muslim-majority countries, although courts have partially blocked the measures from taking effect.

Britain First is a far-right group that opposes multiculturalism and what it calls the "Islamisation" of Britain.

Ms Fransen has been charged with causing religiously aggravated harassment over leaflets and videos that were distributed during a criminal trial earlier this year.

She has separately been charged with using "threatening, abusive or insulting words or behaviour" over a speech she made in Northern Ireland in August. She is currently on bail.

She was convicted last year of religiously aggravated harassment and fined after hurling abuse at a Muslim woman wearing a hijab.

ABC/Reuters