Donald Trump has said American culture is being "ripped apart" by efforts to remove Confederate memorials from parts of the country.
The US president has in recent days been engulfed by criticism of his response to the actions of white supremacists and neo-Nazis in Charlottesville last weekend.
The rally in Virginia was organised to protest the removal of a statue of Robert E Lee, a general who fought for the pro-slavery Confederacy during the US Civil War.
As counter-protesters marched in the city, a car ploughed into them, killing activist Heather Heyer and injuring 19 others.
In an apparent bid to move discussion away from the actions of white supremacists, Mr Trump fired off a series of tweets on Thursday about the future of the statues.
"Sad to see the history and culture of our great country being ripped apart with the removal of our beautiful statues and monuments," the Republican tweeted.
"You can't change history, but you can learn from it."
Prominent Republicans have openly questioned the president's competence and moral leadership following his response to the Charlottesville violence, which he blamed on "both sides".
Senator Bob Corker of Tennessee, who Mr Trump considered for a Cabinet post, declared that "the president has not yet been able to demonstrate the stability nor some of the competence that he needs to" in dealing with crises.
Senator Dan Sullivan of Alaska tweeted: "Anything less than complete & unambiguous condemnation of white supremacists, neo-Nazis and the KKK by the [president] is unacceptable. Period."
Senator Tim Scott of South Carolina said the president's "moral authority is compromised".
Mr Trump dissolved two business councils on Wednesday after the chief executive members began quitting as a result of his comments on the violence.
And the White House said on Thursday it was abandoning plans to form an infrastructure advisory council.
After an initial statement in which he declined to single out the white supremacists and neo-Nazis who took part in the demonstrations, the president was more critical of them on Monday.
But he returned to his initial stance on Tuesday, insisting that "both sides" were to blame.