Later on Wednesday, Mr. Biden held an hourlong virtual roundtable with younger supporters — his team called it a happy hour, though Mr. Biden, who does not drink alcohol, said he had Gatorade on hand — where the former vice president discussed a wide range of subjects raised by young supporters.

He noted his early support for gay marriage — as vice president he spoke out on the subject before President Barack Obama did (Mr. Obama, he said, “gave me a big hug, and said: ‘You told me you weren’t going to be quiet. And you’re right’”). He stressed his support for protecting transgender people. He detailed his views on combating climate change and promised that his administration, should he win the presidency, would reflect the diversity of the nation. He also promised to campaign in states that are traditionally challenging for Democrats, “like North Carolina, Texas, et cetera,” saying that “we haven’t built up a bench.”

“My responsibility is to bring along a new generation of leadership,” he said. “And I start that by the people I pick to serve in my administration.”

And Mr. Biden, 77, twice described himself as something of a transitional figure.

“You all are the answer for us,” he said, a message aimed at younger voters. “And I hope I can just be one of those transition figures that gets to the point where you guys are running the whole show.”

It echoed remarks he made this month in Michigan, where he described himself as a “bridge” to the next generation of leadership.

“I really mean it,” Mr. Biden said on Wednesday, referring to that remark. “That’s why I’ve made the commitment, as I said, for an administration that’s going to look like the country, including choosing a woman running mate. That’s why I wanted to make sure we spent today talking to you.”

Mr. Sanders has also been holding live stream events to talk about the threat from the virus and make the case that his policies on health care and income inequality have become more relevant amid a national health crisis. And as a sitting senator from Vermont, he is part of the Senate’s effort to pass an economic stabilization package.