Editor-at-Large Paul Joseph Watson said it was "not great optics" but also implied it wasn't the president himself who retweeted the video and instead "whoever is running Trump's Twitter account this morning".
Trump, on the other hand, tweeted out to May on Wednesday night asking her not to focus on him.
He said Trump's actions were "a betrayal of the special relationship between our two countries".
Jayda Fransen, deputy leader of anti-immigration Britain First, 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.
Downing Street insisted Theresa May's controversial state visit invitation to Mr Trump still stood, but Whitehall sources acknowledged that no date had been fixed.
Local Government Minister Sajid Javid said Trump had "endorsed the views of a vile, hate-filled racist organisation that hates me and people like me".
May's office rebuked Trump, saying he was "wrong" to have done so.
He said: "You are soon due to visit the United Kingdom".
Republican Senator John McCain said he was "surprised" at the president's tweets. "What do I think about it?"
"A video is a video is a video", Coulter said.
Piers Morgan, a British television host who formerly competed on Trump's reality show "Celebrity Apprentice" and is often sympathetic to Trump and his policies, also blasted the president's retweeting the Britain First videos.
And Foreign Secretary Boris Johnson tweeted that Britain First had "no place" in British society.
The Archbishop, the Rt Rev Justin Welby, called on Mr Trump to delete his retweets and "make clear his opposition to racism and hatred".
"The threat is real and that's what the President is talking about", said Sanders.
The Dutch embassy in Washington took the unusual step of publicly criticising a sitting U.S. president on Twitter.
"@realDonaldTrump Facts do matter".
A spokesperson from the Dutch Public Prosecution Service told the BBC that the person arrested for the attack "was born and raised in the Netherlands" and was not a migrant. "He received and completed his sentence under Dutch law".
Another video is described as showing an Islamist mob pushing a teenager off a rooftop, without any context - it appears to be footage filmed during unrest in Egypt in 2013. In 2015, those involved in the incident were prosecuted, and one man was executed.
"Britain First seeks to divide communities through their use of hateful narratives which peddle lies and stoke tensions".
The group was formed in 2011 and is known for picketing outside mosques.