A bipartisan group of senators is pushing to revive legislation that would bring big changes to federal sentencing laws. The proposal would significantly reduce mandatory minimum sentences for nonviolent drug offenses. The bill will also create a new system for determining which offenders would be eligible for early release and new programs to better prepare them to return to society. A wave of similar criminal justice reforms have been embraced by states across the country.

Advocates of a criminal justice overhaul say that their proposals have gained in popularity since 2015, the last time reform was attempted. A new version of the measure passed the Senate Judiciary Committee 16 to 5 earlier this week. Six of the panel’s 10 Republicans joined every Democrat in backing it.

Now, the legislation depends on Senator Mitch McConnell, Republican of Kentucky and the majority leader, allowing a full Senate vote on the matter. That appears unlikely to happen anytime soon. McConnell, who controls the Senate floor, continues to see the issue as divisive for Republicans, many of whom are averse to lessening criminal penalties of any kind. A small group of Republicans on the committee have already expressed their opposition to the bill.

Senator Charles E. Grassley of Iowa, influential chairman of the Judiciary Committee and lead author of the bill, is trying to change McConnell’s mind. Grassley said in an interview, “This could get broad bipartisan support.” An unlikely coalition of conservative, libertarian and liberal lawmakers, as well as some outside groups, have backed the proposal. Grassley’s legislation currently has the support of more than 20 Democrats and Republicans. Billionaire conservatives Charles G. and David H. Koch and the American Civil Liberties Union have both also expressed their support of the legislation.

The Justice Department under Attorney General Jeff Sessions has ordered federal prosecutors to pursue the toughest possible charges and sentences for crime suspects. Sessions wrote a letter to Grassley earlier this week calling the bill “a grave error.” In it, he wrote, “Passing this legislation to further reduce sentences for drug traffickers in the midst of the worst drug crisis in our nation’s history would make it more difficult to achieve our goals and have potentially dire consequences.”