President Donald Trump and his Democratic challenger Joe Biden traded pre-election barbs Sunday as violent clashes continued to roil the US city of Portland following the fatal shooting of a protestor.

While the US leader tried to characterize Biden as weak on crime, his opponent accused Trump of fanning the flames of violence in a polarized and tense nation.

Saturday's shooting during a pro-Trump rally in the Oregon city followed a week of country-wide protests -- including the cancellation of numerous sporting events -- over the police shooting in Kenosha, Wisconsin of African American Jacob Blake.

The violence in Portland erupted during a rally involving hundreds of vehicles "caravaning throughout downtown Portland," police said. OregonLive reported "clashes" and "tense moments" between demonstrators and counter-protestors.

Photographs from the scene showed the victim wearing a hat with a logo for "Patriot Prayer," described by local media as a far-right group at the center of multiple Portland demonstrations that have ended in violence.

By 10 pm Sunday, about 100 to 150 anti-racism protestors had gathered outside a police building to the east of the city centre, waving signs and occasionally throwing projectiles.

Police declared the gathering an illegal assembly and in a tweet ordered people to leave the scene, warning of arrests and the use of tear gas.

Videos posted online showed about 20 officers rushing from the building to clear the area, and arresting a handful or protestors.

The Portland clashes followed unrest in Kenosha, where prosecutors accused 17-year-old Kyle Rittenhouse of shooting dead two men and wounding another who were protesting against Blake's shooting.

Trump is due to travel on Tuesday to the Midwestern city to meet law enforcement officials and view damage from unrest triggered by Blake's shooting last weekend.

Wisconsin's governor Tony Evers sent the president a letter asking him to reconsider the visit as it "will only hinder our healing," according to US media reports.

'Law and order'

Violence connected to anti-racism protests has become a major issue in the campaign for November's presidential election, with Trump presenting himself as the "law and order" choice and arguing that a Biden presidency would allow left-wing mob rule.

Biden condemned the violence and argued that Trump had played a role in spurring the clashes.

"He is recklessly encouraging violence," the Democratic nominee said in a statement. "He may believe tweeting about law and order makes him strong – but his failure to call on his supporters to stop seeking conflict shows just how weak he is."

Biden's campaign said he will give a speech Monday to address what it called a key question facing voters in November "Are you safe in Donald Trump's America?"  

Trump spent Sunday morning tweeting and retweeting dozens of posts purporting to show violence in Democratic-run cities, and especially Portland.

The president has repeatedly threatened to send federal government forces into the west coast city if Mayor Ted Wheeler does not crack down.

Trump attacked Wheeler, a Democrat, for refusing help from the National Guard, which he said "could solve these problems in less than 1 hour."

"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!"

Wheeler blasted Trump in a press conference Sunday, saying that for nearly four years Americans have had to tolerate what the mayor called Trump's racist attacks on blacks, sexist talk about women, insults toward immigrants and journalists, and now, toward mayors of major US cities.

"Do you seriously wonder, Mr. President, why this is the first time in decades that America has seen this level of violence?," Wheeler said. "It's you who have created the hate and the division."

Wheeler said the convoy that rode through Portland Saturday night was inspired by Trump. "They were supported and energized by the president himself," Wheeler said.

Wheeler had shared an open letter to Trump on Friday in which he said "we know you've reached the conclusion that images of violence or vandalism are your only ticket to re-election."

Senate Homeland Security Committee chairman Ron Johnson, a Republican from Wisconsin, said the violence and loss of life would not stop until law enforcement reasserted control.

"But... when you encourage the disdain for the police you encourage criminals," he told CNN.