Several senior Republican figures have voiced criticism of his comments, including Senator Cory Gardner, who said "Mr President - we must call evil by its name".
The violence left one person dead and dozens more injured.
After being told about the white supremacist objective of the rally, Bloom said she was under the impression her son was merely attending a political rally - not a nationalist march.
Rescue workers and medics tend to many people who were injured when a auto plowed through a crowd of anti-facist counter-demonstrators marching through the downtown shopping district in Charlottesville, Virginia.
"My heart is broken, but I am forever proud of her", Heyer's childhood friend Felicia Correa, who spoke on behalf of the victim's mother, told the Daily News.
Hours later, two State troopers were killed when the helicopter they were flying in as part of a large-scale police effort at the rally crashed into a wooded area outside the city.
"I have a message to all the white supremacists and the Nazis who came to Charlottesville today". The case become a federal one partly because the chief suspect, 20- year-old James Alex Fields, Jr, crossed state lines, from OH to Virginia.
Opposition unity faces hiccups; upset NCP stays away
But so did the lone Gujarat lawmaker from the Bihar Chief Minister's party , which meant he defied his boss' instructions. This is a Congress propaganda to project the NCP as a B-team of the BJP, he also said.
"Our words of condemnation must be followed by actions to ensure those responsible for white supremacist violence are held to account and brought to justice".
Earlier, street brawls erupted between white nationalists and counter-protesters.
The rally stemmed from a long debate in the South over the Confederate battle flag and other symbols of the rebel side in the Civil War, which was fought over slavery.
Disturbances began Friday night during a march through the University of Virginia.
Charlottesville Mayor Mike Signer stated that a vehicle plough into a group of counter-protestors during a gathering for the far-right wing, killing at least one person.
The chaos boiled over at what is believed to be the largest group of white nationalists to come together in a decade: the governor declared a state of emergency, police dressed in riot gear ordered people out and helicopters circled overhead.
The clash was the latest in a series of confrontations after Charlottesville, situated about 100 miles from Washington DC, voted to remove the statue of General Lee.