WASHINGTON (Reuters) - A revised criminal justice reform bill moved closer to a full U.S. Senate vote on Thursday when it gained support from more Republicans after being stalled for months in Congress.

A guard opens the handcuffs of an inmate after he was escorted back into his cell in the East Block during a media tour of California's Death Row at San Quentin State Prison in San Quentin, California December 29, 2015. REUTERS/Stephen Lam

In a legacy-shaping issue for President Barack Obama, the measure’s sponsors announced four new Republican co-sponsor senators and a new version of the bill at a press conference in the Senate. The measure now has 37 co-sponsors, according to Senate Judiciary Committee Chairman Charles Grassley.

Grassley said he had been waiting for the bill to be finalized before asking Senate Majority Leader Mitch McConnell to bring it up for a full Senate vote, but that “it is time for those discussions to start right now.”

As revised, it still lowers mandatory minimum sentences for some non-violent federal drug offenders, but it no longer applies to anyone convicted of a serious violent felony.

That change was a response to conservative critics of the bill, which is central to Obama’s efforts to overhaul the country’s federal criminal justice system and reduce prison overcrowding. That effort has been a rare example of Republican and Democratic agreement in the polarized Congress.

The bill’s advocates have said they hope the revisions and new co-sponsors, such as Republican senators Mark Kirk of Illinois and Steve Daines of Montana, will convince McConnell to bring up the bill for a Senate vote.

Daines and Kirk lent their support after adding minor requirements, including a provision that savings from it go toward purposes such as fighting gangs of national significance.

After a group of conservative Republican senators led by Tom Cotton of Arkansas claimed in January the reforms would release violent felons, the bill’s authors began excising parts of the proposal that eased the sentences of violent criminals.

The bill now includes a new mandatory minimum sentence for crimes involving the opiate fentanyl, mirroring parallel sentencing reforms that await a floor vote in the U.S. House of Representatives.

The House legislation is likely to contain changes to “mens rea” laws that govern criminal intent, said Senator John Cornyn, a sponsor of the Senate bill, at Thursday’s press conference.

Mens rea reform was excluded from the Senate measure because its authors were divided on the issue. Democratic lawmakers generally oppose strengthening mens rea requirements on the grounds it would enable more corporate malfeasance as it is difficult to prove the “intent” of a corporation.

To exclude violent criminals from the Senate bill, the authors removed a section that lowered minimum sentences for unlawful gun owners with three prior convictions for violent felonies or serious drug offenses, known as “armed career criminals.”

Such criminals represent nearly a fifth of the 12,908 current inmates who would have been eligible for resentencing under the old bill, according to the U.S. Sentencing Commission.