As a candidate, Trump called for "a Muslim ban" and, as president, has issued executive orders banning entry from some citizens of multiple countries, although courts have partially blocked them from taking effect.
Jayda Fransen, a leader of the anti-immigrant Britain First group, posted the videos on Wednesday, saying that they showed a group of people who are Muslim beating a teenage boy to death, battering a boy on crutches and destroying a Christian statue.
Reuters was unable to immediately verify the videos.
Fransen, along with the fringe group's head, was arrested in September and charged with causing religiously aggravated harassment over the distribution of leaflets and posting online videos during the court trial involving the case of a number of Muslim men accused and later convicted of rape.
"Donald Trump himself has retweeted these videos and has around 44 million followers! God bless you Trump!" Britain First wrote in a post. Its account has about 24,000 followers.
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