He also appealed to fellow Republicans to "not show weakness" and to resist a House resolution condemning his words.
"I don't have a Racist bone in my body!" Mr Trump exclaimed on Twitter, a day after declaring that "many people agree" with his assessment of the four politicians.
"Those Tweets were NOT Racist," Mr Trump wrote amid a continued backlash to his weekend tweets that the progressive women "go back" to their "broken and crime-infested" countries.
The tweets, which have been widely denounced as racist, were directed at Representatives Ilhan Omar, Alexandria Ocasio-Cortez, Ayanna Pressley and Rashida Tlaib.
All are American citizens, and three of the four were born in the US.
Mr Trump alleged again on Tuesday that the women, who strongly oppose his policies and comments, in reality "hate our country".
The four politicians fired back late on Monday, condemning what they called "xenophobic bigoted remarks" and renewing calls for Democrats to begin impeachment proceedings.
The episode served notice that Mr Trump is willing to again rely on incendiary rhetoric on issues of race and immigration to preserve his political base in the lead-up to the 2020 election.
He shrugged off the criticism.
"It doesn't concern me because many people agree with me," Mr Trump said on Monday at the White House.
"A lot of people love it, by the way."
At the Capitol, there was near unanimous condemnation from Democrats and a rumble of discontent from a subset of Republicans, but notably not from the party's congressional leaders.
House Speaker Nancy Pelosi, who said Mr Trump's campaign slogan truly means he wants to "make America white again", announced on Monday that the House would vote on a resolution condemning his new comments.
The resolution "strongly condemns" Mr Trump's "racist comments" and says they "have legitimised and increased fear and hatred of new Americans and people of colour".
In response, Mr Trump tweeted anew on Tuesday about the four congresswomen: "Why isn't the House voting to rebuke the filthy and hate laced things they have said? Because they are the Radical Left, and the Democrats are afraid to take them on. Sad!"
Republican Senator Mitt Romney, the party's White House nominee in 2012 and now one of the president's most vocal Republican critics, said on Monday that Mr Trump's comments were "destructive, demeaning, and disunifying".
"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.
His words may have been partly meant to widen the divides within the House Democratic caucus, which has been riven by internal debate over how best to oppose his policies.
And while Mr Trump's attacks brought Democrats together in defence of their colleagues, his allies noted he was also having some success in making the progressive politicians the face of their party.
The Republican president questioned whether Democrats should "want to wrap" themselves around this group of four people as he recited a list of the quartet's most controversial statements.
"Nancy Pelosi tried to push them away, but now they are forever wedded to the Democrat Party," he wrote on Tuesday, adding: "See you in 2020!"
At a news conference with her three colleagues, Ms Pressley referred to Mr Trump as "the occupant of our White House" instead of president.
"He does not embody the grace, the empathy, the compassion, the integrity that that office requires and that the American people deserve," she said, encouraging people to "not take the bait".
Ms Pressley said Mr Trump's comments were "a disruptive distraction from the issues of care, concern and consequence to the American people - prescription drug prices, affordable housing, healthcare".
Ms Omar, a naturalised US citizen born in Somalia, accused him of "openly violating" the constitution and sounded the call for impeachment proceedings.
Ms Ocasio-Cortez said Mr Trump "does not know how to defend his policies and so what he does is attack us personally".
The Senate's top Democrat Chuck Schumer said his party would also try to force a vote in the Republican-controlled chamber.