Charlottesville Mayor Mike Singer has urged protesters and counter-protesters to leave.
Charlottesville officials said two people were treated for serious injuries after fights broke out earlier in the leadup to the rally that city officials declared an "unlawful assembly".
McAuliffe said that he spoke with Trump on Saturday and twice told him that "there has got to be a movement in this country to bring people together".
"We condemn in the strongest possible terms this egregious display of hatred, bigotry and violence on many sides", Trump said.
But some of the white nationalists cited Trump's victory as validation for their beliefs, and Trump's critics pointed to the president's racially tinged rhetoric as exploiting the nation's festering racial tension.