The new statement on Sunday comes a day after the president was widely criticized for not explicitly condemning white supremacy in his remarks. The president himself has still not addressed the omission directly.
ABC News asked the president Saturday if he wants the support of white nationalist groups, who say they support him, and whether he feels he's denounced them strongly enough. The president on Saturday did not answer any questions from reporters, however, after he’d taken questions from reporters extensively in prior days.
Trump first tweeted about the violence in Charlottesville Saturday afternoon.
Later on Saturday, speaking from his golf club in New Jersey, Trump made a statement to address the violence.
"We condemn in the strongest possible terms this egregious display of hatred, bigotry and violence on many sides, on many sides," Trump said. "It's been going on for a long time in our country. Not Donald Trump, not Barack Obama, this has been going on for a long, long time. It has no place in America. What is vital now is a swift restoration of law and order and the protection of innocent lives."
On Fox News Sunday, Sen. Lindsay Graham, R-S.C. agreed with Gardner.
"[President Trump] missed an opportunity to be very explicit here," Graham said. "These groups seem to believe they have a friend in Donald Trump in the White House. I don't know why they believe that, but they don't see me as a friend in the Senate, and I would urge the president to dissuade these groups that he's their friend."
Later in the day, a silver Dodge Challenger rammed into a crowd of counter-protesters, sending people "flying," as Sam Becker, 24, describe to the Associated Press. One woman -- 32-year-old Heather Heyer, was killed and 19 others injured, according to Charlottesville City Police Department.
Authorities say the driver of that car was 20-year-old James Alex Fields Jr.. Fields, along with three other individuals, was arrested.
Two Virginia state police officers were killed in connection to the rally. Lieutenant H. Jay Cullen, 48, of Midlothian, Virginia., and Trooper-Pilot Berke M.M. Bates of Quinton, Virginia died when their helicopter crashed as they were "assisting public safety resources with the ongoing situation in Charlottesville," a Virginia State Police spokesperson said in a statement. The crash is still being investigated.
Of the 19 patients from the car incident Saturday that were transported to UVA Medical Center, 10 are in good condition and nine have been discharged, Angela Taylor with UVA Health Systems said on Sunday afternoon. She added that the hospital has treated additional patients related to Saturday’s events, but the facility does not have an exact number of patients.
ABC News' David Caplan contributed reporting for this story.