Demonstrations against racism and police brutality have swept the United States since the death in May of George Floyd, a 46-year-old Black man who died after a Minneapolis police officer knelt on his neck for nearly nine minutes.
Protests have roiled downtown Portland every night for nearly three months following Floyd's death, and police there said they had made arrests after one person was shot to death on Saturday night.
"I condemn violence of every kind by anyone, whether on the left or the right. And I challenge Donald Trump to do the same," Biden said in a statement, adding that "we must not become a country at war with ourselves."
"What does President Trump think will happen when he continues to insist on fanning the flames of hate and division in our society and using the politics of fear to whip up his supporters? He is recklessly encouraging violence," the former vice president added.
Republicans deny Trump is seeking to exacerbate violence with incendiary rhetoric, saying he wants to restore law and order, and accusing Democratic mayors and state governors of losing control of cities rocked by demonstrations that have seen outbreaks of violence, arson and vandalism.
Jason Miller, a senior adviser to Trump's campaign, said on Twitter that Biden had "sat idly by for months, refusing to condemn violence and chaos from his allies in Democrat-run cities."
Trump has emphasized "law and order" to motivate his political base and broaden his support. The Republican president trails Biden in national polls ahead of the Nov. 3 election.
On Friday, Trump said protesters were anarchists, agitators, rioters and looters.
Biden has defended peaceful protesters, saying justice must be done, but he has repeatedly called for an end to violence. His campaign said he would travel to southwestern Pennsylvania on Monday to speak on the safety challenges Americans face under Trump, including chaos in cities, a pandemic and an "upside down" economy.
The president will visit Kenosha, Wisconsin, on Tuesday after new protests erupted there last week following the police shooting of Jacob Blake, another African-American man, multiple times in front of his children, paralyzing him.