In the aftermath of a clash between Black Lives Matter protesters and Trump supporters that left one person dead, Trump railed against Wheeler for openly refusing help from the National Guard.
"Wheeler is incompetent, much like Sleepy Joe Biden," Trump tweeted. "This is not what our great Country wants. They want Safety & Security, and do NOT want to Defund our Police!"
Minutes earlier, the president had tweeted that the "National Guard could solve these problems in less than 1 hour. Local authorities must ask before it is too late."
Trump also retweeted a video where someone speaking before a crowd called the deceased a "Nazi" and appeared to support the killing.
"Our community held its own and took out the trash," the person said, receiving cheers in response.
Police said Saturday evening no suspect information would be immediately released.
An Associated Press freelance photographer heard three gunshots and then observed police medics working on the body of the victim, who appeared to be a white man. The freelancer said the man was wearing a hat bearing the insignia of Patriot Prayer, a right-wing group whose members have frequently clashed with protesters in Portland in the past.
Trump also retweeted several posts that made reference to Wheeler's open letter in which he rejected the National Guard's assistance in quelling the unrest.
Wheeler shared his open letter to Trump on Friday, as protests and violence in his city had already been going on for 90 days.
"On behalf of the City of Portland: No thanks," Wheeler wrote in an open letter to Trump Friday. "We don’t need your politics of division and demagoguery."
The letter continued: "Portlanders are onto you. We have already seen your reckless disregard for human life in your bumbling response to the COVID pandemic. And we know you’ve reached the conclusion that images of violence or vandalism are your only ticket to reelection."
The nightly protests in Portland have turned violent at times, resulting in injuries to both protesters and law enforcement, property damage and dozens of criminal charges.
Trump tweeted Sunday morning that he is prepared to help if Gov. Kate Brown asks.
"The National Guard is Ready, Willing and Able," Trump tweeted Sunday morning. "All the Governor has to do is call!"
On Friday evening, demonstrators staged a sit-in inside the lobby of Wheeler’s condominium building while others held a loud concert outside.
The protesters said they wouldn’t leave until Wheeler meets with them over their demands that he resign, reduce the Portland Police Bureau budget and never vote to increase police spending.
Fox News' Marisa Schultz and Brie Stimson and The Associated Press contributed to this report.