The Prime Minister's official spokesman said it was "wrong" for Mr Trump to have promoted the videos posted on twitter by the deputy leader of Britain First, an organisation which Theresa May's spokesman said "peddles lies".
But a planned state visit which has yet to be scheduled will not be cancelled, he added.
The spokesman said: "Britain First seeks to divide communities through their use of hateful narratives which peddle lies and stoke tensions.
"They cause anxiety to law-abiding people. British people overwhelmingly reject the prejudiced rhetoric of the far right, which is the antithesis of the values which this country represents: decency, tolerance and respect.
"It is wrong for the President to have done this." Downing Street revealed that Mrs May, who is on a tour of the Middle East, had just completed a visit to Iraq.
The US President shared three videos with his 43.6 million followers that target Muslims and were posted by Britain First leader Jayda Fransen earlier this week. Headings on at least two of the videos, which suggest the footage shows violence by Muslims, have already been shown to be misleading or wrong.
The White House press secretary defending the President's actions, telling journalists in Washington: "Whether it's a real video, the threat is real. His goal is to promote strong border security and strong national security."
Ms Fransen's organisation has shared misleading videos on Facebook and Twitter at least 10 previous occasions. Despite being alerted to the misleading nature of those videos, the organisations have declined to remove them.
Ms Fransen, Britain First leader Paul Golding and the official Britain First accounts are all 'verified' on Facebook and Twitter, which critics say lends them legitimacy.