US authorities will investigate on Sunday the violence stemming from a white nationalist rally a day earlier that killed one person, injured more than 30, and challenged U.S. President Donald Trump's leadership.

The unrest in the southern college town presented Trump with a domestic crisis, with many on both left and right criticizing him for waiting too long to address it and then, when he did so, failing to explicitly condemn the white-supremacist marchers who ignited the melee.

"Absolutely we are going to have further demonstrations in Charlottesville, because our constitutional rights are being denied," said Jason Kessler, identified by civil rights groups as a white nationalist blogger. He did not specify when.

Kessler organized the "Unite the Right" rally in Charlottesville against a plan to remove a statue to Confederate war hero Robert E. Lee from a park, saying in a telephone interview those who came in support will not back down.

Four people were arrested in the violence, including James Fields, a 20-year-old white man from Ohio being held in jail on suspicion of plowing a car into a crowd of counter-protesters on Saturday, killing a 32 year-old woman and injuring 19, five of them critically.

Police have not yet provided a motive for the incident but U.S. attorneys and the Federal Bureau of Investigation have opened a civil rights investigation into the crash, an FBI field office said.

Federal authorities were also looking into a helicopter crash on Saturday that killed two Virginia state policemen aiding efforts to quell the clashes.

Virginia Governor Terry McAuliffe, a Democrat, declared an emergency and halted the white nationalist rally planned for Saturday but that did not stop the violence.

About 15 people were injured after rival groups fought pitched battles using fists, rocks and pepper spray.

"Please go home and never come back," was McAuliffe's message for the white supremacists, delivered at a news conference.

"There is no place for you here, there is no place for you in America," he added.

Trump said "many sides" were involved in the Charlottesville incidents, remarks that drew fire from across the political spectrum for not specifically denouncing white nationalists.

"We condemn, in the strongest possible terms, this egregious display of hatred, bigotry and violence on many sides," Trump told reporters at his New Jersey golf course on Saturday.

The planned rally stemmed from a long debate in the U.S. South over the Confederate battle flag and other symbols of the rebel side in the Civil War, which was fought over slavery.

The Charlottesville violence is the latest clash between far-rightists, some of whom have claimed allegiance to Trump, and the president's opponents since his January inauguration, when black-clad anti-Trump protesters in Washington smashed windows, torched cars and clashed with police, leading to more than 200 arrests.

About two dozen people were arrested in Charlottesville in July when the Ku Klux Klan rallied against the plan to remove the Lee statue. Torch-wielding white nationalists also demonstrated in May against the removal.