Thousands of Donald Trump supporters alleging electoral fraud protested in several US cities and there were isolated scuffles with counter-demonstrators.
In Washington DC, more than 20 people were arrested and four people were stabbed, police said.
Mr Trump lost the November 3 election but is yet to concede.
The Electoral College, the system which elects US presidents, is due to endorse Mr Biden’s victory on Monday.
Mr Biden won 306 votes to Mr Trump’s 232 in the Electoral College, and gained over seven million more votes than his Republican rival in the popular vote.
In the nation’s capital, police sought to keep the two sides apart, a strategy that included sealing off Black Lives Matter Plaza where counter-demonstrators had gathered.
Pro-Trump demonstrators, rallying under the banner of “Stop the Steal”, were joined by members of the far-right Proud Boys, dressed in yellow and black, many wearing bullet-proof vests.
Mr Trump caused controversy by saying the group should “stand back and stand by” during a September presidential debate, though he later condemned “all white supremacists”.
As night fell insults were yelled between groups of protesters resulting in violence.
The stabbings took place near the downtown Harry’s Bar, but it was not clear which group those injured belonged to, according to the Washington Post.
Make America Great Again (MAGA) protesters, who support Mr Trump, were captured on video tearing down a Black Lives Matter sign from a church, pouring petrol on it and setting it alight.
Rallies also took place in Olympia, the capital of Washington state, Atlanta and St Paul, Minnesota. Police in Olympia said one person had been shot and three arrested as rival groups clashed.
The Washington DC rally attracted several thousand Trump-supporters but it was smaller than a similar event on 14 November. Few participants wore masks despite Covid-19 restrictions.
There were speeches by Mr Trump’s now pardoned former National Security Advisor, Michael Flynn, and Sebastian Gorka, another former White House official.
The president’s latest legal defeat came on Friday when the Supreme Court rejected an unprecedented attempt to throw out results in four battleground states which Mr Biden won. Mr Trump has now lost more than 50 cases linked to the election.