The tiny extremist group, meanwhile, appeared delighted at the publicity boost from a leader with almost 44 million Twitter followers.
Trump drew sharp criticism from both government and opposition politicians in Britain after retweeting three videos from the account of deputy Britain First leader Jayda Fransen purporting to show violence by Muslims.
In response, Labour Party lawmaker David Lammy tweeted: "@realDonaldTrump you are not welcome in my country and my city." Another Labour legislator, Chuka Umunna, said Trump's invitation to visit Britain "should be withdrawn."
Labour lawmaker Chris Bryant went so far as saying that Trump should be arrested for inciting religious hatred if he came to the U.K.
May announced in January that Trump had accepted an invitation for a state visit to Britain, one of the highest honors the country can bestow on a foreign leader. Almost a year later, no date has been set, and opponents of Trump have vowed to stage large protests if he does come.
May's spokesman, James Slack, said it was "wrong" for the president to have retweeted Britain First. He said the group seeks to divide communities through its use of "hateful narratives which peddle lies and stoke tensions."
May's office said the state visit would not be canceled, but Trump's online activity drew rebukes from government ranks.
Communities Secretary Sajid Javid, who is Muslim, tweeted that Trump "has endorsed the views of a vile, hate-filled racist organization that hates me and people like me. He is wrong and I refuse to let it go and say nothing."
Brushing off the criticism in an evening tweet, Trump said May instead of focusing on him should "focus on the destructive Radical Islamic Terrorism that is taking place within the United Kingdom."
Founded in 2011, Britain First opposes multiculturalism and what it calls the "Islamization" of Britain. Small but publicity-savvy, it has staged direct-action protests at mosques and is active on social media. The group regularly posts inflammatory videos purporting to show violence by Muslims, without context or supporting information.
Fransen, 31, was convicted last year of religiously aggravated harassment after hurling abuse at a Muslim woman wearing a hijab during what was billed as a "Christian patrol" in the town of Luton, north of London. She currently faces four unrelated counts of harassment relating to leaflets and videos and a separate charge of hate speech.
Trump's retweets were a major publicity boost for the group, whose own Twitter account is followed by about 24,000 others.
Fransen tweeted: "God bless you Trump! God bless America!" in capital letters to her followers, whose number grew by several thousand to about 60,000 in the hours after the boost from the president.
British authorities have warned about a growing threat from violent far-right extremism, and recently charged the leader of another white supremacist group with plotting to kill a lawmaker.
In June 2016, Labour lawmaker Jo Cox was shot and stabbed to death by Thomas Mair, who shouted "Britain first" as he attacked her.
The legislator's widower, Brendan Cox, tweeted Wednesday: "Spreading hatred has consequences & the President should be ashamed of himself."
London Mayor Sadiq Khan, a Muslim who has been the target of inaccurate criticism by Trump about his supposedly lax approach to extremist violence, also criticized the president.
"Britain First is a vile, hate-fuelled organization whose views should be condemned, not amplified," Khan said.
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