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 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,” Mr Trump tweeted.

Mr Trump’s original tweet has since been taken down.

Mr Trump later deleted the tweet and wrote a fresh one, this time addressing it to the correct Twitter account.

“@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!” he wrote.

.@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

Ms May is yet to respond to Mr Trump’s tweets.

President Trump retweeted a string of inflammatory videos from a fringe British political group purporting to show violence being committed by Muslims.

The tweets drew a sharp condemnation from Ms May’s office, which said it was “wrong for the president to have done this”.

Mr Trump had turned away from taxes, North Korea and other issues facing his administration to share the three videos tweeted by Jayda Fransen, deputy leader of the British group. It was not clear what drew him to the videos, though one had been shared by conservative commentator Ann Coulter the day before.

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.

The tweets read: “VIDEO: Islamist mob pushes teenage boy off roof and beats him to death!” and “VIDEO: Muslim Destroys a Statue of Virgin Mary!” and “VIDEO: Muslim migrant beats up Dutch boy on crutches!”

His promotion of the videos came two days after he mocked Senator Elizabeth Warren as “Pocahontas” during an Oval Office event with Native American veterans, drawing criticism from of Native American war veterans and politicians of both major parties.

Mr Trump’s retweets have given a wide platform to the previously obscure group. The videos were each shared more than 10,000 times, and Ms Fransen picked up nearly 10,000 Twitter followers in the hours following Trump’s retweets. She thanked him on Twitter, saying “GOD BLESS YOU TRUMP!”

Former Ku Klux Klan leader David Duke also welcomed the videos, tweeting that Mr Trump was being “condemned for showing us what the fake news media WON’T. Thank God for Trump! That’s why we love him!”

– with AAP