Mayor Mike Signer said recent clashes over race and the Confederacy had turned "equestrian statues into lightning rods" and urged Democratic Governor Terry McAuliffe to convene a special session of the General Assembly.
Signer's statement came nearly a week after white supremacists descended on the city and violently clashed with counter protesters. One woman was killed on Saturday when a car plowed into a crowd of people there to condemn what is believed to be the largest gathering of white supremacists in a decade.
Charlottesville's plans to remove the statue are in the midst of a legal challenge. A law passed in 1998 forbids local governments from removing or damaging war monuments, but there remains legal ambiguity about whether that applies to statues erected before the law was passed.
McAuliffe spokesman Brian Coy said the governor won't call a special session while the issue is being decided in court.
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"The governor hopes the court will rule in the city's favour soon and encourages Mayor Signer to focus on that important litigation rather than a redundant emergency session," Coy said.
Speaking on ABC's "Good Morning America," Susan Bro said she initially missed the first few calls to her from the White House. But she said "now I will not" talk to the president after a news conference in which Trump equated violence by white supremacists at the rally with violence by those protesting the rally.
Bro's daughter, 32-year-old Heather Heyer, was killed and 19 others were injured when the driver rammed a car into a crowd of demonstrators. An Ohio man, James Alex Fields Jr, has been arrested and charged with murder and other offences.
"You can't wash this one away by shaking my hand and saying 'I'm sorry,'" Bro said of the president. She also advised Trump to "think before you speak.