Mr Biden made the remarks during a speech in the battleground state of Pennsylvania as both candidates shift the blame onto each other over the current civil unrest across the US. National protests erupted in response to the recent police shooting of Jacob Blake in Kenosha, Wisconsin.
That shooting has led to several days of demonstrations in the city, which resulted in the deaths of two people, allegedly by an armed vigilante.
Mr Biden’s speech comes as tensions rise between the two candidates over clashes in Portland, Oregon, where a man linked to a right-wing group was shot dead on Saturday.
Also on Saturday, a pro-Trump rally taking place in the city clashed with Black Lives Matter protesters.
Speaking on Monday at Carnegie Mellon University in Pittsburgh, Mr Biden said: “The simple truth is Donald Trump failed to protect America. “So now he’s trying to scare America.”
Mr Biden added that the president “long ago forfeited any moral leadership in this country”.
He said: “He can’t stop the violence – because for years he has fomented it.
“We need justice in America. And we need safety in America.
“We are facing multiple crises – crises that, under Donald Trump, keep multiplying.
READ MORE: Donald Trump shut down by Biden over failure to stop civil unrest
In a statement following Mr Biden’s speech, Tim Murtaugh, the Trump campaign’s communications director, said: “As predicted, Joe Biden today failed to condemn the left-wing mobs burning, looting, and terrorising American cities.”
However, Mr Biden had previously published a statement on his official website condemning the events taking place in Portland.
The statement reads: “The deadly violence we saw overnight in Portland is unacceptable.
“Shooting in the streets of a great American city is unacceptable. I condemn this violence unequivocally.
“I condemn violence of every kind by any one, whether on the left or the right.”