Trump also retweeted those who blamed the city's Democratic mayor for the death.
"The people of Portland, like all other cities & parts of our great Country, want Law & Order," Trump later tweeted. "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!"
Trump has throughout the summer cast American cities as under siege by violence and lawlessness, despite the fact that most of the demonstrations against racial injustice have been largely peaceful.
With about nine weeks until Election Day, some of his advisers see an aggressive "law and order" message as the best way for the president to turn voters against his Democratic rival, Joe Biden, and regain the support of suburban voters, particularly women, who have abandoned him.
But Democrats accuse Trump of rooting for unrest and trying to stoke further violence for political gain instead of seeking to ratchet down tensions.
"He may think that war in our streets is good for his reelection chances, but that is not presidential leadership or even basic human compassion," Biden said in a statement responding to the shooting, in which he "unequivocally" condemned violence on all sides, while accusing Trump of "recklessly encouraging" it.
Portland Mayor Ted Wheeler, a Democrat, blamed Trump for the tensions.
"Do you seriously wonder, Mr. President, why this is the first time in decades that America has seen this level of violence?" he asked at a televised news conference. "It's you who have created the hate and the division."
Trump, who appeared to be watching, responded with real-time tweets labeling Wheeler a "wacky Radical Left Do Nothing Democrat."
After a reporter told Wheeler about the tweet, the mayor shot back, "I'd appreciate that the president support us or stay the hell out of the way."
Trump has cast the upcoming election as clash between "law and order" and anarchy, and he has denounced protesters as "thugs" while sharply defending police. That theme was front-and-center at last week's Republican National Convention, which used recent protest footage to paint a foreboding and violent picture of the future if Biden denies Trump a second term.
Trump is expected to continue to hit that theme when he travels Tuesday to Kenosha, Wisconsin, where tensions are still raw after police shot Jacob Blake, a 29-year-old Black man, in the back seven times, leaving him paralyzed. The shooting has ignited new demonstrations against racial injustice and police brutality months after George Floyd's death at the hands of a Minneapolis police officer touched off a wider reckoning on race.
Trump will be meeting with law enforcement officers and "surveying" the damage in the city, where businesses have been vandalized and some buildings burned during demonstrations, White House spokesman Judd Deere announced.
But Wisconsin Gov. Tony Evers, a Democrat, asked Trump to reconsider in a letter Sunday.
"I, along with other community leaders who have reached out, are concerned about what your presence will mean for Kenosha and our state. I am concerned your presence will only hinder our healing. I am concerned your presence will only delay our work to overcome division and move forward together," Evers wrote in the letter, obtained by The Associated Press.
Earlier Sunday, Wisconsin Lt. Gov. Mandela Barnes, also expressed concerns about the visit. "I don't know how, given any of the previous statements that the president made, that he intends to come here to be helpful. And we absolutely don't need that right now," Barnes said in an interview with CNN.
Rep. Karen Bass, a California Democrat who leads the Congressional Black Caucus, said Trump is "doing everything he can to fan the flames."
"I think his visit has one purpose, and one purpose only. And that is to agitate things and to make things worse," Bass said Sunday on CNN's "State of the Union." "It is clear his campaign is all about law and order. It is a throwback to the past. And he's going to do everything to disrupt law and order in this time period."
Deere responded to the critics saying, "The only people to blame for the violence and riots in our streets are liberal politicians and their incompetent policies that have failed to get control of these destructive situations."
It took days for Trump to weigh in on Blake's shooting, which was captured on cellphone video, and even then he had little to say.
"Well, I'm looking into it very strongly. I'll be getting reports," he said in an interview in New Hampshire Friday. "It was not a good sight. I didn't like the sight of it, certainly, and I think most people would agree with that."
Trump offered similar words — "We're looking at it very, very carefully" — when asked Saturday about Kyle Rittenhouse, the white 17-year-old who has been charged with fatally shooting two protesters and wounding a third Tuesday after he traveled to Kenosha, apparently to defend the city from protesters. Attorneys representing Rittenhouse, who was seen walking with an assault-style rifle, have said he acted in self-defense.
But Trump on Sunday appeared to lend support to the teenager when he liked a retweet of a series of messages that began, "Kyle Rittenhouse is a good example of why I decided to vote for Trump."
The circumstances of Saturday night's shooting in Portland remain unclear. Video from the city shows sporadic fighting between the groups, with Trump supporters firing paintball pellets at opponents and using bear spray as counterprotesters threw things at the Trump caravan.
The man killed was a member of Patriot Prayer, a right-wing group whose members have frequently clashed with protesters in Portland in the past, its founder, Joey Gibson, said Sunday. He identified the victim as Aaron "Jay" Danielson and called him a "good friend," but provided no details. Danielson apparently also went by the name Jay Bishop, according to Patriot Prayer's Facebook page.
Trump retweeted the victim's name and wrote, "Rest in peace Jay!"
The White House and its allies, meanwhile, continued to blame local leaders for allowing the protests to rage on night after night.
"When you encourage the disdain for the police, you encourage criminals. When you do little or nothing to stop rioting, you encourage anarchy. So when you are encouraging criminals and anarchy, people's lives are lost," Republican Sen. Ron Johnson of Wisconsin said on CNN's "State of the Union."
