"That's why I'm running," the former Vice President added.
The likely Democratic Party nominee for President denounced violence in America's cities as a response to the Floyd killing, urging a conversation about the plight of minorities in America.
"There's no place for violence, no place for looting or destroying property or burning churches or destroying businesses," Biden said.
Biden's speech marked his first major campaign appearance since mid-March, when the arrival of the Coronavirus suddenly shut down the 2020 campaign.
It was the third straight day that the Floyd story had drawn Biden out of his home in Delaware - where he had been sidelined by the virus outbreak.
On Sunday, Biden visited the site of a protest in his home town of Wilmington and spoke with members of the black community.
On Monday, Biden visited a local church, and met with black clergy from the area.
"These are difficult days for the country," Biden said in a Monday live stream with mayors from Los Angeles, Chicago, and Atlanta, as Biden denounced the street violence around the nation.
"Violence that endangers lives, guts local businesses is no way forward," Biden said, as he joined calls by Democrats for a more direct conversation on what led to the death of Floyd, at the hands of a Minneapolis police officer.
"What are the reforms, if any, within police departments that we should be focusing on," Biden suggested to the mayors.