United States President Donald Trump hit back at British Prime Minister Theresa May last night after she criticised him for retweeting three anti-Muslim videos posted by a British far-right group.

Trump wrote on Twitter: "Theresa, 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 @theresamay, which is not the Twitter account of the Prime Minister, before correcting the mistake about 20 minutes later.

"Wrong twitter handle. And that's just the start," Carrie Symonds, director of communications at the Conservative Party, tweeted.

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Trump earlier in the day had shared three posts by Jayda Fransen, deputy leader of Britain First. The posts included unverified videos titled "Muslim Destroys a Statue of Virgin Mary!" and "Muslim migrant beats up Dutch boy on crutches!"

May said Trump was "wrong" to share them with his followers.

Her official spokesman said Britain First sought to divide communities through its use of "hateful narratives which peddle lies and stoke tensions".

"It is wrong for the President to have done this," the spokesman said.

However, the spokesman said plans for Trump's state visit remain in place.

White House spokeswoman Sarah Huckabee Sanders said Trump was simply promoting border security and suggested that verifying the content was not a top concern.

"Whether it's a real video, the threat is real and that is what the President is talking about," she said.

Brendan Cox, the widower of British MP Jo Cox, responded in a tweet, saying: "Trump has legitimised the far-right in his own country, now he's trying to do it in ours. Spreading hatred has consequences & the President should be ashamed of himself."

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Labour MP Jo Cox was murdered by a right-wing extremist last year in the lead-up to the Brexit referendum.

At least one of the videos Trump retweeted — "Muslim migrant beats up Dutch boy on crutches" — has been proven wrong.

The incident was said to have taken place in Monnickendam. A 16-year-old was arrested but was not a migrant or a Muslim, but an "ordinary Dutchman", according to the Dutch reports.

The video titled "Islamist mob pushes teenage boy off roof and beats him to death!" first surfaced in 2013 and was recorded in Egypt, amid violence following the overthrow of Islamist president Mohamed Morsi. The perpetrators were later sentenced to death.