A top Republican senator joined other members of his party meanwhile in criticizing the president, saying Trump had not displayed the stability or competence needed to lead the country and risks putting it in "great peril."
Shrugging off a barrage of bipartisan criticism, Trump waded back into the charged racial debate over monuments to the pro-slavery Civil War South with a volley of early morning tweets.
"Sad to see the history and culture of our great country being ripped apart with the removal of our beautiful statues and monuments," Trump said.
Trump has come under fire from Republicans and Democrats alike for insisting that anti-racism protestors were equally to blame for violence last weekend at a rally staged by neo-Nazis and white supremacists in Charlottesville, Virginia, to protest the planned removal of a statue of Confederate general Robert E. Lee.
A 32-year-old woman was killed and 19 other people injured when an Ohio man suspected of being a white nationalist drove his car into a crowd of counter-protesters.
Trump -- who rose to political prominence by casting doubt on whether Barack Obama, America's first black president, was born in the United States -- has been deluged with demands to unambiguously disavow white hate groups, whose members have been emboldened by his election.
Trump did condemn neo-Nazis and the Ku Klux Klan on several occasions this week -- but many say he did not go far enough. He has earned rebukes from across the political spectrum, even from former presidents George H.W. Bush and George W. Bush.
'Please fix this'
Senator Bob Corker, chairman of the Senate Foreign Relations Committee, on Thursday became the latest member of Trump's Republican Party to criticize the president.
"I don't think that the president has appropriately spoken to the nation on this issue," the senator from Tennessee said.
"Helping inspire divisions because it generates support from your political base is not a formula for causing our nation to advance."
"The president has not yet been able to demonstrate the stability nor some of the competence that he needs to demonstrate in order to be successful," Corker said.
"And without the things that I just mentioned happening our nation is going to go through great peril."
The president was forced to scrap two White House economic advisory councils on Wednesday as top businessmen began abandoning him in protest.
A White House official said Thursday plans to form a presidential advisory council on infrastructure had also been dropped.
Along with repealing Obamacare, Trump had promised tax reform and a $1 trillion plan to improve the country's infrastructure.
Efforts to repeal Obama's signature health plan failed, however, and the tax and infrastructure programs have made little headway.
With moves to dismantle Confederate monuments gaining momentum, Nancy Pelosi, the Democratic leader in the House of Representatives, called for Confederate statues to be removed from the US Capitol.
"There is no room for celebrating the violent bigotry of the men of the Confederacy in the hallowed halls of the United States Capitol."
Trump made it clear though on Thursday that he opposed removing Confederate monuments.
"You can't change history, but you can learn from it. Robert E Lee, Stonewall Jackson -- who's next, Washington, Jefferson? So foolish!" Trump said.
"Also the beauty that is being taken out of our cities, towns and parks will be greatly missed and never able to be comparably replaced!"
Lee commanded the Army of Northern Virginia and General Thomas "Stonewall" Jackson was one of his top lieutenants, while George Washington and Thomas Jefferson were among the Founding Fathers of the United States.
Trump hits critics, media
Trump's chief strategist, Steve Bannon, told The New York Times meanwhile he believed the president's views were shared by many Americans.
"President Trump, by asking, 'Where does this all end' - Washington, Jefferson, Lincoln - connects with the American people about their history, culture and traditions," Bannon said.
A poll released Thursday would appear to support the view that many Americans oppose removing the monuments to the Confederacy.
The NPR/PBS/NewsHour/Marist poll of 1,125 adults asked whether Confederate statues should remain as a historical symbol or be removed because they offend some people.
Sixty-two percent said they should remain while 27 percent said they should be taken down.
Trump on Thursday also lashed out at a frequent Republican critic, Senator Lindsey Graham of South Carolina, and accused the media of distorting his views.
"The public is learning (even more so) how dishonest the Fake News is," he said. "They totally misrepresent what I say about hate, bigotry. etc. Shame!"
"Publicity seeking Lindsey Graham falsely stated that I said there is moral equivalency between the KKK, neo-Nazis & white supremacists... and people like Ms. Heyer," Trump said.
Heather Heyer, 32, was the woman killed by the suspected white nationalist in Charlottesville.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)
Get the latest election news, live updates and election schedule for Lok Sabha Elections 2019 on ndtv.com/elections. Like us on Facebook or follow us on Twitter and Instagram for updates from each of the 543 parliamentary seats for the 2019 Indian general elections.