WASHINGTON — During Tuesday’s luncheon with fellow U.S. Senate Democrats, Connecticut’s Chris Murphy said efforts to reach a deal with Republicans on new gun control measures were moving in a positive direction.

He asked for members to give him more time to firm up an agreement and encouraged them not to add pressure on members of either party while negotiations continue. Georgia Sens. Jon Ossoff and Raphael Warnock both said they want to give Murphy the space he needs to get the results they seek.

“It sounds like some bipartisan progress is being made,” Ossoff said Tuesday afternoon. “So, I’m going to decline to negotiate via the press and in public and give that bipartisan negotiation the space that it needs to produce some result that I will consider.”

Like Ossoff, Warnock said he is chosen not to speak publicly about what he thinks any gun safety measure put on the Senate floor should entail. Instead, he backed efforts to reach an agreement that could gain the support of at least 10 Republicans so that it is not killed by a filibuster. Both senators said getting new gun control measures passed is a priority in light of recent high-profile mass shootings, including a massacre at an elementary school in Uvalde, Texas, two weeks ago.

“I don’t know that it’s helpful is this moment to draw red lines,” Warnock said. “I want to see us get something done. I want to see us break the logjam. I think it would be a signal moment of moral failure if the Senate does absolutely nothing when 19 babies are slaughtered and two teachers in the classroom.”

U.S. House Democrats this week are expected to pass a slate of gun control measures that include raising the minimum age for purchasing a semiautomatic rifle from 18 to 21 years old, banning large-capacity magazines, further restricting bump stocks that allow guns to be fired rapidly, and further regulating “ghost guns,” which are untraceable firearms that can be bought online and assembled at home.

House Democrats are also expected to take a vote on a bill sponsored by Georgia U.S. Rep. Lucy McBath that would create a federal “red flag” law that allows guns to be temporarily removed from people deemed by a judge to be a threat to themselves or others. That law would also incentives states to create their own “red flag” legislation. Georgia is not among the 19 states that already have such laws on the books.

Speaker Nancy Pelosi has also said the House will at some point take a vote on reinstating a ban on assault weapons.

If Murphy and the bipartisan group of senators, including lead Republican Sen. John Cornyn of Texas, are able to reach an agreement, their legislation is expected to be much narrower in scope. Expanded background checks, red flag laws, improving school safety and a waiting period for 18- to 21-year-olds buying certain guns appear to have the most traction in the Senate.

Warnock said he knows Democrats will need to adjust their expectations of what the Senate can accomplish on the issue with the filibuster in mind.

“What we get passed is not going to be everything we want,” he said. “But we need to break this logjam.”