Mr. Sanders is seeking to cut into Mr. Biden’s base of older caucusgoers in Iowa, seizing on an issue of great significance to them.

“Let’s be honest, Joe,” Mr. Sanders wrote as he tweeted out his own video on Tuesday, using Mr. Biden’s own words from years ago about freezing Social Security. “One of us fought for decades to cut Social Security, and one of us didn’t. But don’t take it from me. Take it from you.”

On MSNBC on Wednesday, Mr. Biden broached a different policy issue, gun control, where Mr. Sanders’s record has previously drawn scrutiny. Mr. Biden suggested that his past statements about Social Security were being taken out of context, and proceeded to cite Mr. Sanders’s record on guns.

“It’s like my going back and pointing out how Bernie voted against the Brady Bill five times while I was trying to get it passed when he was in the House, or how he voted to, you know, protect gun manufacturers,” Mr. Biden said. “It’s the only group in America you can’t sue. I mean, he’s made up for that. He’s indicated that was past.”

Mr. Biden was referring to Mr. Sanders’s votes against the Brady Bill, which required background checks for gun purchases, in the 1990s, as well as his 2005 vote for a bill that shielded gun manufacturers and dealers from liability lawsuits. Mr. Sanders faced criticism for those votes from Hillary Clinton during the 2016 Democratic primary.

Asked about his opposition to the Brady Bill in a recent interview with the editorial board of The New York Times, Mr. Sanders said the world had since “changed” and mass shootings had proliferated.

“I come from a state that until two years ago had no gun control at all. Zero. O.K. People of Vermont have changed, and I certainly have changed on that issue,” he said. “There is now in Vermont, and all over this country, disgust at the level of mass shootings and gun violence in general. And I will have an administration that will have a gun policy second to none.”

Sydney Ember contributed reporting from Des Moines, and Thomas Kaplan from Washington.