President Obama convened a meeting of more than a dozen congressional Republicans and Democrats Thursday, in an effort to bolster a fragile bipartisan coalition working to reform the criminal justice system.

The House and Senate have been working to craft legislation to reduce mandatory minimum sentences for drug offenders, as well as to revamp aspects of federal incarceration. The Senate Judiciary Committee passed a comprehensive bill on a bipartisan 15-5 vote in October; the House Judiciary Committee has passed five separate measures by voice vote in recent weeks.

But there are a few major differences between the two chambers’ approaches. Most significantly, one of the House bills — the Criminal Code Improvement Act — would require prosecutors in cases as wide-ranging as food tainting and corporate pollution to prove that defendants “knew, or had reason to believe, the conduct was unlawful,” otherwise known as “mens rea.”

That measure has angered many Democrats, who argue that it could block criminal prosecution of some corporate entities — including those owned by Koch Industries, which has helped mobilize conservative support for the overall reform effort. Obama specifically asked lawmakers to remove the provision, according to individuals familiar with the meeting, though House Republicans argued that it was a critical component for conservatives.

“We believe that invites a lot of controversy and delay into our agreement, and the House feels just the opposite,” said Senate Minority Whip Richard J. Durbin (D-Ill.), who attended the White House meeting and co-authored the Senate criminal justice bill.

Sen. John Cornyn (R-Tex.), another co-author of the bill, said that while “nothing was decided” in the more than hour-and-a-half session, he was “very optimistic” after participating in it.

“I think it was all a very positive, bipartisan, bicameral, executive, legislative meeting,” Cornyn said, adding that although “there was not consensus” on that issue, there might be a way to work it out in a conference between the two chambers. “But I think part of the message was, ‘Let’s take the things where there is consensus, get that done.’ ”

A spokeswoman for House Judiciary Committee Chairman Bob Goodlatte (R-Va.) declined to comment on the meeting. She noted that the House panel has passed bills on issues including modifying sentencing guidelines and eliminating statutes in the U.S. Code that subject violators to criminal penalties for trivial conduct. The committee will take up measures on prisons, civil asset forfeiture, and criminal procedures and policing in the coming weeks, she added.

Durbin said “we have a good chance” of passing legislation in early 2016, so lawmakers can work out their differences “and send it to the president before midpoint of next year.”

Senate Judiciary Committee Chairman Charles E. Grassley (R-Iowa), who helped craft the Senate bill and also met with the president, said the meeting was less about “the path forward” than how to get the two competing proposals brought up for floor votes in the House and Senate.

Obama also pressed for specific numbers on how many individuals would benefit overall from the two proposals, people familiar with the meeting said, because the proposals introduce new sentences even as they reduce some mandatory minimums.

The White House has continued to make the case for criminal justice reform in public as well, hosting an event at the complex’s South Court Auditorium on Thursday morning, which activists from across the ideological spectrum attended. Grover Norquist, president of the conservative group Americans for Tax Reform, was in the audience along with Michael B. Jordan, who starred in HBO’s “The Wire” and is currently appearing in the Rocky spinoff “Creed,” and David Simon, who created “The Wire.”

In an e-mail after his speech, Norquist said that he spoke about the use of excessive fines by law enforcement officials in Ferguson, Mo., and elsewhere. “If you turn the police into IRS collection agents, it doesn’t promote good community relations,” he said, adding that these communities “deployed police to maximize revenue not citizen safety.”

Speaking at Thursday’s event, White House senior adviser Valerie Jarrett said the time has come to reexamine policies “that have a disparate impact, particularly on people of color or those who are poor. And let’s face it, that’s who we’re incarcerating.”

“And there is momentum building,” Jarrett said. “And I don’t often say that I believe Congress will act, but in this instance, I do.”

But as Grassley noted in an interview, lawmakers will ultimately determine whether the president’s initiative is passed into law.

“It’s what happens up here that will make a difference,” he said.