Senate Minority Leader Nancy Pelosi issued a statement saying, in part, "The vile beliefs of the perpetrators of this violence insult our fundamental American values and must be condemned in the strongest terms".
Police are still investigating the cause of the crash.
Officials told the Associated Press the crash was linked to the rally, although they did not elaborate on how the crash was connected.
His comments were criticised for not specifically denouncing the white supremacists while condemning the "display of hatred, bigotry and violence on many sides".
The president's silence had been noticeable Friday night, as a few hundred tiki torch-bearing white supremacists - mostly young men - paraded through the University of Virginia campus while chanting racist taunts and flaunting Nazi paraphernalia. The driver, identified as James Alex Fields, Jr., is being charged with second degree murder and multiple other felony counts. The goal of the controversial event was to unify the far-right wing and "affirm the right of Southerners and white people to organize for their interests", according to its Facebook page. Go home. You are not wanted in this great commonwealth.
President Trump's remarks were panned by members of both political parties, who said the white nationalists, neo-Nazis and neo-Confederates were at fault for the violence.
A gray auto with OH license plates hit a crowd near the city's downtown mall, killing a 32-year-old woman.
Right-wing blogger Jason Kessler organized Saturday's rally to protest the city's decision to remove a statue of Confederate General Robert E. Lee.
The violence we've witnessed today is not who we are as a country.
North Korea talk drags stocks lower; gold, yen rise
Benchmark US 10-year notes last rose 6/32 in price to yield 2.1905 per cent, from 2.211 per cent late on Thursday. After touching a more than two-month high, spot gold last added 0.1 percent to $1,287.18 an ounce.
Shares hit by US-North Korea tensions
Penney slumped 16.56 percent to a record low after the retailer reported a bigger-than-expected quarterly loss. Meanwhile, the dollar USDJPY, -0.31% fetched ¥109.69, compared with ¥110.31 late Tuesday.
Wall Street lower on US-North Korea tensions
The data comes amid tepid inflation that has remained below the Federal Reserve's 2 percent target, despite low unemployment. The local currency closed at 1,143.50 won against the USA dollar, down 1.50 won from the previous session's close.