President Donald Trump retweeted videos Wednesday posted online by a British far-right nationalist that purport to show violent acts carried out by Muslim men, drawing rebukes from a pair of U.S. allies along with civil-rights advocates in the U.S.

Mr. Trump used the social-media platform to circulate a trio of tweets posted by Jayda Fransen, the deputy leader of Britain First, a small anti-Islam group in the U.K. that describes itself as a political party and a street movement. She was convicted in 2016 for religiously aggravated...