He made the plea at a press conference in which he also blamed the president for inciting violence, calling him out for four years of what he called racist and bigoted hate speech.
Mr Wheeler said: "President Trump, for four years we've had to live with you and your racist attacks on black people. We learned early about your sexist attitudes towards women. We've had to endure clips of you mocking a disabled man; we've had to listen to your anti-democratic attacks on journalists; we've read your tweets slamming private citizens to the point of receiving death threats; and we've listened to your attacks on immigrants."
He added: "Do you seriously wonder, Mr President, why this is the first time in decades that America has seen this level of violence? It's you – who have created the hate and the division.
"You bring no peace. You bring no respect to our democracy."
In a further jab he said: "You've tried to divide us more than any other figure in modern history and now you want me to stop the violence you helped create. What America needs is for you to be stopped so that we can come back together as one America."
Mayor Wheeler said that he mourned the fact that a man had been killed on the street on Saturday night, and denounced the violence.
The man, who has not yet been publicly identified, but was wearing a cap withe the insignia of far-right group Patriot Prayer, was shot in the street while a convoy of vehicles driven by Trump supporters was driven through the city, where protests in favour of racial justice have raged for weeks.
On Sunday morning the president had fired off a barrage of tweets and retweets, some of them insulting Mr Wheeler. One of his retweets, from an account title Tiff, reads: "Ted Wheeler is the useless f***ing idiot and comic relief that gets everyone killed in every disaster movie." The president added: "Tone down the language, but TRUE!"
After apparently spending much of the day golfing in Virginia, Mr Trump reacted to the mayor's press conference with fury as it was still going on.
He tweeted: "Ted Wheeler, the wacky Radical Left Do Nothing Democrat Mayor of Portland, who has watched great death and destruction of his City during his tenure, thinks this lawless situation should go on forever. Wrong! Portland will never recover with a fool for a Mayor.
"He tried mixing with the Agitators and Anarchists and they mocked him. He would like to blame me and the Federal Government for going in, but he hasn't seen anything yet. We have only been there with a small group to defend our U.S. Courthouse, because he couldn't do it."
He added: "The people of Portland, like all other cities & parts of our great Country, want Law & Order. The Radical Left Democrat Mayors, like the dummy running Portland, or the guy right now in his basement unwilling to lead or even speak out against crime, will never be able to do it!"
Mr Wheeler was asked about the tweets during the press conference.
He responded by asking the president directly how he thought such comments could be "constructive". Instead he called for Mr Trump to condemn violence and to "work together to help move this country forward".
On Sunday afternoon, Joe Biden issued a statement condemning the violence and called on Mr Trump to do the same.
The Democratic presidential candidate wrote: "It does not matter if you find the political views of your opponents abhorrent, any loss of life is a tragedy. Today there is another family grieving in America, and Jill and I offer our deepest condolences."
He added: "We must not become a country at war with ourselves. A country that accepts the killing of fellow Americans who do not agree with you. A country that vows vengeance toward one another.
"But that is the America that President Trump wants us to be, the America he believes we are."
He said the president was "recklessly encouraging violence".