A top Senate Republican signaled that progress is being made as lawmakers from both sides of the aisle are meeting to discuss gun legislation in the wake of the mass shooting at a Uvalde, Texas, elementary school last week.

A bipartisan group of senators, including Sens. John Cornyn (R-TX), Chris Murphy (D-CT), Kyrsten Sinema (D-AZ), and Thom Tillis (R-NC), met virtually earlier this week to discuss drafting the legislation. The lawmakers are expected to reconvene later for further discussion, said Cornyn, who is the senior senator from the state where the deadly Uvalde shooting took place.

ONE DEAD AND TWO INJURED IN SHOOTING AT NEW ORLEANS HIGH SCHOOL GRADUATION

"Senators Murphy, Sinema, Tillis, and I had a very constructive conversation about the best response to the horrific events in Uvalde last week," Cornyn said in a statement. "We've asked our staff to continue to work together to address some of the details that we hope to be able to discuss at some point soon."

Some compromises may be in the works, including red flag laws, expansive background checks, and safer gun storage, said Murphy, whose state suffered the 2012 Sandy Hook school shooting that killed 26.

“It is true, you know. Republicans are not willing to support everything that I support, like banning assault weapons,” Murphy told CBS’s Face the Nation on Sunday. “But I really think that we could pass something that saves lives and breaks this logjam that we've had for 30 years, proving to Republicans that if you vote to tighten the nation's gun laws, the sky doesn't fall for you politically. In fact, you probably will get a lot of new additional supporters.”

The House Judiciary Committee is set to consider eight pieces of gun legislation Thursday as part of the Protecting Our Kids Act, according to a committee aide. Lawmakers are expected to advance the legislation to the House floor for a vote by next week, while the Senate will be a tougher hurdle to clear.

If passed, the legislation would change the minimum age to purchase a semi-automatic rifle to 21 years old, criminalize the importation, sale, manufacturing, transfer, or possession of a large-capacity magazine, establish regulations for storing firearms in residential facilities, and apply current firearms regulations to “ghost guns,” among other reforms.

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The May 24 shooting in Uvalde in which officials said an 18-year-old gunman killed 21 people at Robb Elementary School, including 19 children and two teachers, follows another mass shooting in Buffalo, New York, earlier this month that killed 10 people. The gunmen in both shootings bought their rifles legally at 18.

Cornyn's counterpart from Texas, GOP Sen. Ted Cruz, has argued gun restrictions will not be effective. “That doesn’t work. It’s not effective. It doesn’t prevent crime,” Cruz said last week.

President Joe Biden visited the families of the Uvalde victims, telling reporters Sunday that the pain was “palpable.” The president indicated he would speak with Congress about possible gun legislation, although it’s not yet clear when he plans to do so.

"When the time comes, he will get involved," White House press secretary Karine Jean-Pierre said Tuesday.