U.S. President Joe Biden delivers remarks on the monthly U.S. jobs report, at the Rehoboth Beach Convention Center, in Rehoboth Beach, Delaware, U.S., June 3, 2022. REUTERS/Tom Brenner
CNN  — 

President Joe Biden on Tuesday met with Sen. Chris Murphy, one of the top Democratic lawmakers negotiating on gun reform, at the White House for an update as talks intensify on Capitol Hill.

“We’re entering a pretty critical stage so I thought it would be important to just come over and fill him in on where our discussions are,” Murphy told CNN as he entered the West Wing.

Asked who scheduled Tuesday’s meeting, the Connecticut Democrat said, “We thought it was mutually beneficial to have a conversation.”

The White House has been taking a hands-off approach as negotiators continue to discuss potential legislation. Biden is giving negotiations the “space that it needs,” White House press secretary Karine Jean-Pierre said Monday, adding that Biden is “encouraged” by the talks.

Murphy said he has been in touch with White House officials and Biden “pretty regularly” and said he appreciates the space the President has given senators to carry out negotiations.

Following the meeting, Murphy said he and Biden spoke for about a half hour about the outlines of the ongoing gun reform negotiations.

“Nobody knows the Senate better than President Biden and he knows that we’ve gotta work out our compromise on our own,” Murphy told reporters outside the West Wing after the meeting. “It’s important to keep him posted on our discussions because ultimately we need the President to support it and sign the legislation.”

Murphy said his goal remains to reach a deal by the end of this week but said Senate Majority Leader Chuck Schumer “has been clear that if we need some extra time to dot the I’s and cross the T’s, we’ll get it.”

“We had a good conversation,” Murphy said of his meeting with Biden. “Obviously we’ve still got work to do in the Senate and I’m grateful that the White House is giving us the space necessary to get a deal done.”

Lawmakers have expressed optimism that a deal for a narrow, targeted bill could be reached as soon as the end of this week or next. The four main bipartisan senators – Republican Sens. John Cornyn of Texas and Thom Tillis of North Carolina and Murphy and Sen. Kyrsten Sinema of Arizona – met for negotiations late into the evening Monday. Murphy told reporters following the meeting that they are making progress but there is still work to do.

Murphy said Tuesday he is aiming to get an agreement by the end of the week, but insisted there are “no artificial deadlines” and said senators would take more time if needed.

“My goal is to get an agreement by the end of the week. This is the most politically complicated and emotionally fraught issue we work on. But I think we can try and get something done in the next few days,” he said.

That progress specifically involves looking at the juvenile records of 18 to 21 year olds trying to purchase a semi-automatic weapon. Tillis indicated that there could be a potential waiting period for individuals trying to buy those kinds of weapons.

Incentivizing states to pass red flag laws, school safety, investments in mental health care and access, and the potential waiting period for 18 to 21 year olds buying guns like AR-15s are measures that are still on the table as the negotiations progress.

Murphy conceded during an appearance on ABC’s “The View” earlier Tuesday that Democrats will not get “everything that we want” in a potential package.

“I’m sober-minded about our chances,” he said when pressed on whether this time was different in the aftermath of multiple mass shootings across the country. But, he added, there is “momentum” and “urgency” this time and he is “deeply hopeful” a framework can ultimately be reached to make some progress against gun violence.

CNN’s Manu Raju, Lauren Fox, and Ted Barrett contributed to this report.