The legislation proposes an extensive set of changes in federal sentencing requirements. Those changes include a reduction in mandatory minimum sentencing to five years from 10 for qualified cases and to 15 from 20 in others, and the so-called three-strike penalty is reduced to 25 years from life imprisonment.

Many of the new rules could be applied retroactively, and an estimated 6,500 people now in prison would be able to petition for new sentences should the legislation become law.

The legislation would also ban solitary confinement for juveniles in nearly all cases, and allow those sentenced as juveniles to seek a reduction in sentencing after 20 years.

The bill would put some new mandatory minimum sentences in place for those convicted of interstate domestic violence, or of providing weapons or other material to terrorists or to certain countries. While those crimes are relatively rare, the new sentences could help secure votes from lawmakers who do not want to be seen as being soft on crime.

If the authors wish to push the legislation through this year, it will require an aggressive effort and a decision by Senator Mitch McConnell, Republican of Kentucky and the majority leader, to make the measure a priority. Mr. Grassley said he had to meet with the committee to determine the path forward, but the legislation could be considered by the panel this month. Full congressional consideration could also be kicked into 2016.

The leadership shake-up in the House, where a similar bill is being put together, could influence the proposal’s fate, as well. Speaker John A. Boehner of Ohio, whose resignation from Congress is effective at the end of October, has strongly endorsed the general concept of a sentencing overhaul, but it is unclear what the view of the new leadership team will be.

Despite broad support for the legislation, the effort to work out the details slowed in the Senate, and some advocates and lawmakers worried that the negotiations would fall apart. Some tough-on-crime statements from Republican presidential candidates and a highly publicized increase in murders in cities across the country also raised fears that the effort could stall, even though it is aimed at nonviolent crimes.