Donald Trump and Portland's mayor have blamed each other for the violence on the Oregon city's streets after a man was shot dead following clashes between the US president's supporters and left-wing protesters.
Trump on Sunday called Wheeler a "fool" on Twitter and said to "Bring in the National Guard!" while Wheeler blamed Trump for creating such a toxic environment.
"It's you who have created the hate and the division," the Democratic mayor said of Trump. "You've tried to divide us more than any other figure in modern history. And now you want me to stop the violence that you helped create."
Trump had earlier issued a flurry of tweets and retweets, including several blaming Wheeler for the death on Saturday night and one in which the president appeared to be encouraging his supporters to move into Portland. "GREAT PATRIOTS!" Trump wrote as he shared video of his supporters driving into Portland to confront the protesters.
It came as Joey Gibson, the head of the right-wing group Patriot Prayer, told the Associated Press the man who was shot to death was a member and a "good friend", although he did not identify him.
Gibson said he was in Portland on Saturday night when the Trump supporters clashed with Black Lives Matter protesters downtown. Gibson arrived at the scene of the shooting shortly after it happened and video from the scene showed he was briefly corralled in a nearby gas station by angry protesters.
"I can't say much right now. All I can do is verify that he was a good friend and a supporter of Patriot Prayer," Gibson said of the shooting victim in a text exchange. He said he would make a fuller statement later on Sunday.
Police issued a plea for any information related to the killing, including videos, photos or eyewitness accounts. The shooting happened about 15 minutes after a caravan of about 600 vehicles that were part of a pro-Trump rally left downtown.
It was not clear if the shooting was related to the clashes between Trump supporters and counter-protesters in Portland, which has become a flashpoint in the national Black Lives Matter protests since George Floyd was killed in May and an increasing centrepiece in Trump's law-and-order re-election campaign theme.
An Associated Press freelance photographer heard three gunshots and then saw police medics attending to the victim, who appeared to be a white man. The freelancer said the man was wearing a hat bearing the insignia of Patriot Prayer.
Governor Kate Brown, a Democrat who has feuded with Trump, said in a statement that Trump had "encouraged division and stoked violence" in American cities - now including Portland.
In the two hours following the shooting, protesters gathered downtown and there was sporadic fighting and vandalism, police said. Ten people were arrested.