The altercation came after Mr Trump responded directly to her assertion, tweeting: '@Theresa_May, don't focus on me, focus on the destructive Radical Islamic Terrorism that is taking place within the United Kingdom. "The threat needs to be addressed", she said. "And I'm very clear that retweeting from Britain First was the wrong thing to do".
It came as Sir Kim Darroch, the British ambassador to the United States, revealed he had made a formal complaint to the White House.
Her comments are the first direct challenge made to President Trump since a Downing Street statement on Wednesday.
After Trump retweeted a series of anti-Muslim videos earlier this week, May took to Twitter to call him out.
"But the move angered the U.S. leader, who tweeted: "@Theresa_May, don't focus on me, focus on the destructive Radical Islamic Terrorism that is taking place within the United Kingdom. America is "doing fine", POTUS said.More news: Demolition blast fails to bring down notoriously decrepit Silverdome
She said she had been deluged with tweets from Donald Trump's followers - despite only having six of her own. In the United Kingdom we take the far-right very seriously and that's why we ensure we deal with these threats and this extremism wherever it comes and whatever its source'.
Several MPs have demanded that a state visit invitation, extended to the US President on behalf of Queen Elizabeth II, be withdrawn in protest. Problem is, he initially picked on the wrong Theresa May.
The visit, penciled in for February 26-27, has remained unchanged despite the recent diplomatic row over Trump's controversial re-tweets of anti-Muslim videos by a British far-right organisation.
'British Muslims are peaceful and law-abiding citizens, ' Kim Darroch tweeted.
"I haven't been able to leave my house".