The plan arrives just over a week before the second round of presidential debates.

In the first round last month, Mr. Biden, who continues to enjoy strong support from African-American voters, found himself on the defensive, as Senator Kamala Harris of California ripped into his record on civil rights. She criticized his opposition to many busing measures dating to the 1970s and his warm recollections last month about his working relationships with segregationists in the Senate. Mr. Biden has expressed regret for those remarks but has been unapologetic about many other aspects of his record.

Next week, Mr. Biden will again share the debate stage with Ms. Harris, and will face off for the first time with Senator Cory Booker of New Jersey, who has also criticized Mr. Biden over his remarks about segregationist senators.

On Tuesday, Mr. Booker, who, like Ms. Harris, is black, highlighted Mr. Biden’s role in shaping the very criminal justice system his plan now seeks to reform. He rebuked Mr. Biden for his record and sought to contrast it with his own in a potential preview of clashes to come in the next debate.

“Joe Biden had more than 40 years to get this right,” Mr. Booker said in a statement. “The proud architect of a failed system is not the right person to fix it. The 1994 crime bill accelerated mass incarceration and inflicted immeasurable harm on black, brown and low-income communities. While it’s encouraging to see Vice President Biden finally come around to supporting many of the ideas I and others have proposed, his plan falls short of the transformative change our broken criminal justice system needs.”

Mr. Biden’s proposal calls for empowering the Justice Department to “root out unconstitutional or unlawful policing” and for an independent task force focused on prosecutorial discretion.

For people who are re-entering society after serving prison sentences, Mr. Biden sets a goal of “ensuring” that all formerly incarcerated people have housing when they are released. That initiative would start with instructing the Department of Housing and Urban Development to “only contract with entities that are open to housing individuals looking for a second chance,” as well as increasing funding for transitional housing.

Mr. Biden is also urging a $20 billion competitive grant program aimed at preventing incarceration and crime at the state and local level by addressing issues such as “illiteracy and child abuse that are correlated with incarceration.” It comes with the stipulation that “states will have to eliminate mandatory minimums for nonviolent crimes, institute earned credit programs and take other steps to reduce incarceration rates without impacting public safety.”