The US president took to Twitter once again to defend his comments, saying they were "not racist" and urged other Republicans not to condemn his rhetoric.
In a tweet on Tuesday, Mr Trump said: "Those Tweets were NOT Racist. I don’t have a Racist bone in my body! The so-called vote to be taken is a Democrat con game.
"Republicans should not show “weakness” and fall into their trap. This should be a vote on the filthy language, statements and lies told by the Democrat.....
".....Congresswomen, who I truly believe, based on their actions, hate our Country. Get a list of the HORRIBLE things they have said. Omar is polling at 8%, Cortez at 21%. Nancy Pelosi tried to push them away, but now they are forever wedded to the Democrat Party. See you in 2020!"
The Republican has repeatedly defended the remarks he made about Alexandria Ocasio-Cortez, Ilhan Omar, Ayanna Pressley and Rashida Tlaib, where he said they "can leave" the US to "go back and help fix the totally broken and crime infested places from which they came".
The president said condemnation of his comments, including belatedly from some Republicans, “doesn’t concern me because many people agree with me”.
The congresswomen have fired back at what they called his “xenophobic bigoted remarks” and said it was time for impeachment.
New York congresswoman Alexandria Ocasio-Cortez said Mr Trump “does not know how to defend his policies and so what he does is attack us personally”.
But, in typically confrontational style, Mr Trump hit Twitter on Monday to say: “The Dems were trying to distance themselves from the four ‘progressives’, but now they are forced to embrace them.
“That means they are endorsing socialism, hate of Israel and the USA! Not good for the Democrats!”
The president responded to questions at the White House after his Sunday tweet assailing the politicians, all of whom are US citizens and three of whom were born there.
He has been roundly criticised by Democrats who labelled his remarks racist and divisive. A smattering of Republicans also have objected, although most leading Republicans have been silent.
Mr Trump said on Monday that if the politicians “hate our country” they “can leave” it.
“If you’re not happy in the US, if you’re complaining all the time, you can leave, you can leave right now,” he said.
The politicians’ criticism has been largely aimed at Mr Trump and his administration’s policies and actions.
It was yet another sign that Mr Trump, who won the presidency in 2016 in part by energising disaffected voters with incendiary racial rhetoric, has no intention of backing away from that strategy going in 2020.
Earlier, Mr Trump made it clear he had no intention of backing down, asking on Twitter when “the Radical Left Congresswomen” would “apologise to our country, the people of Israel and even to the office of the president, for the foul language they have used, and the terrible things they have said”.
“So many people are angry at them & their horrible & disgusting actions!” he wrote.
Asked whether Mr Trump’s comments were racist, Marc Short, chief of staff to vice president Mike Pence, defended the president, telling reporters he had been responding to “very specific” comments made by congresswoman Ilhan Omar of Minnesota, who was born in Somalia, and was not making a “universal statement”.
But Mr Trump did not make that distinction in his tweets.
He cited “congresswomen” — an almost-certain reference to a group of women who have labelled themselves “the squad”, that includes Ms Omar, Ms Ocasio-Cortez, Ayanna Pressley of Massachusetts and Rashida Tlaib of Michigan.
At a news conference, Ms Pressley said Americans should “not take the bait” from Mr Trump and should instead focus on their own agenda, even as the politicians called for Democrats to take up impeachment proceedings against the president.
Ms Omar ignited a bipartisan uproar in Washington several months ago when she suggested that some members of Congress support Israel because of money, while Ms Tlaib riled up a supportive crowd by calling the president a profane name and predicting he would be removed from office.
Mr Trump on Monday singled out Ms Omar, in particular, accusing her of having “hatred” for Israel, and expressing “love” for “enemies like al-Qaeda”.
“These are people that, in my opinion, hate our country,” he said.
House Speaker Nancy Pelosi said Mr Trump wants to “make America white again”, while Ms Ocasio-Cortez said the president “can’t conceive of an America that includes us”.
“Mr President, the country I ‘come from’, & the country we all swear to, is the United States,” she tweeted.
Ms Omar also addressed herself directly to Mr Trump in a tweet, writing: “You are stoking white nationalism (because) you are angry that people like us are serving in Congress and fighting against your hate-filled agenda”.
Ms Pelosi announced on Monday that the House would be holding a vote on a resolution condemning Mr Trump’s comments.
Former vice president Joe Biden, the Democratic presidential front-runner, tweeted that Mr Trump “continues to spew hateful rhetoric, sow division, and stoke racial tensions for his own political gain”.
Elizabeth Warren, another Democratic presidential candidate, tweeted: “Let’s be clear about what this vile comment is: A racist and xenophobic attack on Democratic congresswomen.”
Among the few Republican politicians commenting, Pete Olson of Texas said Mr Trump’s Sunday tweet was “not reflective of the values of the 1,000,000+ people” in his district.
“We are proud to be the most diverse congressional district in America. I urge our President immediately disavow his comments,” he wrote.