In taking that position, he is embracing a past proposal from Mr. Sanders, though one that is less expansive than what Mr. Sanders is currently advocating. Mr. Biden’s proposal is similar to one offered in the last presidential race by Hillary Clinton, who in the summer of 2016 proposed tuition-free college for many students after her primary battle with Mr. Sanders.

“Senator Sanders, Senator Warren and Vice President Biden share the goal of strengthening college as a reliable pathway to the middle class and ensuring that no American is unable to reach or to stay in the middle class because of insurmountable debt,” Mr. Biden’s campaign said in a news release, making the outreach to supporters of Mr. Sanders and Ms. Warren explicit.

In the 2020 campaign, Mr. Sanders, of Vermont, has proposed making public colleges and universities tuition-free for all students, regardless of family income. Before dropping out of the race, Ms. Warren had also proposed making public colleges and universities tuition-free without an income limit. Earlier in the campaign, Mr. Biden proposed making two years of community college tuition-free.

In 2017, Mr. Sanders introduced legislation that included a proposal to get rid of tuition and fees at four-year public colleges and universities for students from families making up to $125,000. The Biden campaign said Mr. Biden was adopting that proposal.

Mr. Sanders responded to Mr. Biden’s proposal by arguing it did not go far enough.

“It’s great that Joe Biden is now supporting a position that was in the Democratic platform four years ago,” Mr. Sanders said in a statement. “Now we have to go much further. We need to make all public universities, colleges and trade schools tuition-free for everyone like our high schools are. We need to cancel all student debt. And we can fund it with a small tax on Wall Street speculation.”