Trump hits out at May for criticising him over video tweets
"Don't focus on me, focus on the destructive Radical Islamic Terrorism that is taking place within the United Kingdom," Trump wrote on Twitter, BBC reported on Thursday.
The US President earlier retweeted three inflammatory videos posted online by a British far-right group.
May's spokesman said it was "wrong for the president to have done this".
The US and the UK are close allies and often described as having a "special relationship".
The videos shared by Trump, who has more than 40 million followers, were initially posted by Jayda Fransen, the deputy leader of Britain First, a group founded by former members of the far-right British National Party (BNP).
Fransen has been charged in the UK with using "threatening, abusive or insulting words or behaviour".
The first tweet from Fransen claims to show a Muslim migrant attacking a man on crutches. This was followed by two more videos of people Fransen claims to be Muslim.
White House spokeswoman Sarah Sanders said May and other world leaders knew that "these are real threats that we have to talk about".
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