Theresa May has told Donald Trump that sharing anti-Muslim videos posted online by far-right group Britain First "was the wrong thing to do".
But Mrs May indicated she is not withdrawing her invitation for the US President to come to the UK on a state visit, despite widespread calls for the trip to be cancelled.
Mr Trump sparked outrage in the UK by retweeting three videos from the far-right group, purportedly showing violent acts by Muslims.
In response to a statement from Downing Street describing his actions as "wrong", Mr Trump told Mrs May to "focus on terrorism" and not him.
But Number 10 hit back, saying Mrs May is "fully focused on dealing with extremism".
And speaking in Jordan on Thursday, Mrs May said: "The fact that we work together does not mean that we are afraid to say when we think that the United States have got it wrong and to be very clear with them.
"I am very clear that retweeting from Britain First was the wrong thing to do."
Asked whether she regarded Mr Trump as a fit person to be hosted by the Queen on a state visit, she said: "An invitation for a state visit has been extended and has been accepted. We have yet to set a date."
Mrs May described Britain First as "a hateful organisation" which "seeks to spread division and mistrust among our communities"
"As Prime Minister, I am very clear about the priority that I give to dealing with the challenge of the threat of terrorism...and extremism from whatever source they come," she said.
Britain's Ambassador to the US, Kim Darroch, said he complained directly with the White House over Mr Trump's tweets.
Facing an Urgent Question in the House of Commons on Thursday, Home Secretary Amber Rudd said Mr Trump was "wrong" to retweet the posts from Britain's First's deputy leader.
The question was brought by Labour MP Stephen Doughty, who said by sharing the tweets Mr Trump was "either a racist, incompetent or unthinking, or all three".
He called on the government to cancel Mr Trump's state visit, but the home secretary responded: "The invitation for the visit has been extended and accepted but the dates and precise arrangements have yet to be agreed."
After the prime minister's spokesman last night said Mr Trump's retweets were "wrong", the president lashed out, telling Theresa May: "Don’t focus on me, focus on the destructive Radical Islamic Terrorism that is taking place within the United Kingdom."
Asked about Mr Trump's Twitter rebuke to Mrs May, the Prime Minister's official spokesman told reporters: "Over her time as home secretary and as Prime Minister - and obviously in the wake of the tragic events over the summer - the Prime Minister is fully focused on dealing with extremism."
Mr Trump has been widely condemned for his actions, with repeated calls for his planned state visit to be cancelled, while Communities Secretary Sajid Javid said the president had "endorsed the views of a vile, hate-filled racist organisation".
In the Commons, Mr Doughty told the home secretary: "This is the president of the United States, sharing with millions inflammatory and divisive content, deliberately posted to sow hatred and division, by, as the home secretary says, a convicted criminal who is facing further charges, who represents a vile, fascist organisation, who seeks to spread hatred and violence in person and online.
"By sharing it, he is either a racist, incompetent or unthinking, or all three."
Labour's shadow home secretary Diane Abbott said Mr Trump's actions were an "attack on the values of this country".