Washington, Sep 1 (IANS): US President Donald Trump and his Democratic rival Joe Biden have been accusing one another over violence that has erupted at protests in Portland, Oregon.

A man linked to a right-wing group was killed on Saturday, as elsewhere in the city a pro-Trump rally clashed with Black Lives Matter protesters.

Trump called participants of the rally "great patriots" and blamed the city's Democratic mayor for the unrest. Biden in turn accused Trump of "rooting for chaos and violence", the BBC reported.

In a campaign speech in the city of Pittsburgh on Monday, the Democratic candidate said: "Fires are burning and we have a president who fans the flames rather than fighting the flames. But we must not burn. We have to build."

Portland has become a flashpoint for demonstrations against police brutality and racism since the police killing of African-American George Floyd in Minneapolis on May 25 triggered a wave of national and international outrage.

Media reports say a man who calls himself an anti-fascist is being investigated over Saturday's deadly shooting, while the founder of the right-wing group Patriot Prayer identified the victim as a supporter.

Trump on Sunday re-tweeted what appeared to be the dead man's name along with the message "Rest in Peace".

Police have not publicly named the suspect or the victim, or specified whether the shooting was directly linked to the clashes.

The President is set to visit the city of Kenosha, Wisconsin, on Tuesday amid anger there over the police shooting of black man Jacob Blake.

Trump has blamed Portland's Democratic Mayor Ted Wheeler for the unrest.

"Portland will never recover with a fool for a mayor," he wrote on Twitter on Sunday as he suggested sending federal forces to the city.

He also accused Biden of being "unwilling to lead".

Trump continued on Monday, describing Portland as "a mess" and repeating calls for "LAW & ORDER".

"If this joke of a mayor doesn't clean it up, we will go in and do it for them," he wrote.

In another tweet he said "Radical Left Mayors & Governors of Cities where this crazy violence is taking place have lost control of their 'Movement'."

"It wasn't supposed to be like this, but the Anarchists & Agitators got carried away and don't listen anymore - even forced Slow Joe out of basement," he added in reference to his Democratic rival.

On Sunday, Biden said the president "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".