US President Donald Trump has sparked shock and outrage on social media after sharing videos posted by a British far-right activist, known for her anti-Muslim rhetoric, on Twitter.

The US leader shared three videos by Britain First deputy leader Jayda Fransen, purporting to show Muslims carrying out beatings or acts of vandalism.

Britain First's Fransen, who in 2016 was convicted by a British court for harassing a woman wearing a hijab, is banned by court order from entering mosques in the UK.

Together with other activists from the far-right group, Fransen took part in regular mosque "invasions".

Thomas Mair, the killer of British MP Jo Cox is reported to have shouted the group's name after stabbing the Labour Party politician.

One of the tweets shared by Trump shows a video of a teenage boy beating up another teen boy on crutches. The incident happened in May this year in the Dutch town of Monnickendam.

After the video was posted on Dutch social media in May, police arrested two Dutch teens from Monnickendam and neighbouring town, Edam-Volendam, in connection to the beating. It was never confirmed that the individual in the video was Muslim or a migrant.

Trump's decision to share the videos was sharply condemned by rights groups.

"By his unconscionable and irresponsible actions this morning, President Trump is clearly telling members of his base that they should hate Islam and Muslims," said Nihad Awad, national executive director of the Council of American-Islamic Relations.

The Muslim Council of Britain urged the country's authorities to distance themselves from Trump and his comments.

The Muslim Council of Britain comments on President Trump sharing anti-Muslim videos from the far right pic.twitter.com/rYOlUkLxUj — MCB (@MuslimCouncil) November 29, 2017

The American Civil Liberties Union also said that "Trump's prejudice against Muslims reveals itself at every turn".

Trump's prejudice against Muslims reveals itself at every turn—with today's tweets meant to gin up fear and bias, with statements like "Islam hates us," and with every version of the Muslim ban. — ACLU (@ACLU) November 29, 2017

In Britain, the official spokesperson for Prime Minister Theresa May, said Trump was "wrong" to share the videos.

"Britain First seeks to divide communities by their use of hateful narratives that peddle lies and stoke tensions. They cause anxiety to law-abiding people," said a statement reported by UK media.

"British people overwhelmingly reject the prejudiced rhetoric of the far right which is the antithesis of the values this country represents, decency, tolerance and respect. It is wrong for the president to have done this."

Jeremy Corbyn, leader of the Labour Party, the country's second-biggest political force, condemned Trump's retweets as "abhorrent, dangerous and a threat to our society".

I hope our Government will condemn far-right retweets by Donald Trump. They are abhorrent, dangerous and a threat to our society. — Jeremy Corbyn (@jeremycorbyn) November 29, 2017

Many others on social media also voiced anger that the holder of such a high office would share material from a far-right activist.

"Trump sharing Britain First. Let that sink in. The President of the United States is promoting a fascist, racist, extremist hate group whose leaders have been arrested and convicted. He is no ally or friend of ours. (Donald Trump) you are not welcome in my country and my city," British Labour Party MP David Lammy tweeted.

Brian Klass, an academic at the London School of Economics, wrote: "Here in the UK, Britain First is (correctly) seen as a neo-Fascist hate group. They are beyond the fringe extremists. Their leaders have been arrested and convicted for inciting hatred, including the horrible racist woman that Trump re-tweeted multiple times."

Donald Trump has been retweeting Britain First leader and rampant anti-Muslim activist Jayda Fransen. See how her online following has spiked following recent terror attacks: https://t.co/Zx2aj0KzZk pic.twitter.com/5I8llyLm4M — HOPE not hate (@hopenothate) November 29, 2017

Wednesday's retweets are not the first time Trump has shared or made comments that are considered racist or discriminatory.

On Monday, speaking to a group of Native American veterans, Trump referred to US Senator Elizabeth Warren who claims Native American ancestry as "Pocahontas", after a historic Native American figure.

Trump also campaigned on a platform of banning Muslim entry to the US and the surveillance of mosques in the country.

Shortly after taking office, he signed an executive order banning nationals from seven Muslim-majority countries from entering the US. After court challenges, the ban was revised and now includes restrictions on citizens from six Muslim-majority countries, as well as North Korea and Venezuela.