A new proposal in Washington to expand background checks for gun sales could hold promise, Sen. Pat Toomey (R., Pa.) said Friday, saying he remains in talks with President Donald Trump and Attorney General William Barr over the long-debated issue.

After nearly two months of discussion in Washington, lawmakers and Trump are considering the proposal from Barr, who has been talking with members of Congress about a way forward.

Since 31 people were killed in back-to-back mass shootings in Ohio and Texas in early August, Republicans have been waiting for a signal from Trump on whether he’ll support expanded background checks, which gun-control advocates say could reduce violence. Barr’s proposal, which the White House has not yet endorsed, added to confusion over the issue on Capitol Hill this week.

But Toomey, speaking to reporters in Philadelphia on Friday, said Barr was exploring “very thoughtful” ideas, Trump remains engaged, and at least some Republicans are “reconsidering” the issue.

“There is a momentum I haven’t perceived in quite a long time,” said Toomey, who along with Sens. Joe Manchin (D., W. Va.) and Chris Murphy (D., Conn.) met with Barr for a “very constructive, fairly lengthy conversation” on Wednesday and spoke with Trump on Thursday at the White House.

Barr’s proposal would be less restrictive than both the background-check bill passed by the House in February and the bill Toomey and Manchin attempted to pass in 2013 and 2015. The attorney general’s plan would expand background checks while aiming to appease conservative opponents by weakening documentation requirements and making it easier for people living in rural areas to obtain checks.

Gun control advocates argue that expanding background checks to all commercial gun sales, including those made online or at gun shows, would prevent firearms from being bought by people prohibited from owning them. Toomey said the policy could have stopped the man who recently shot 25 people, killing seven, in Odessa, Texas, from obtaining his weapon.

Toomey, who faces a reelection campaign in two years and is one of the few Republicans to support expanded background checks, has had several conversations with Trump and Barr about the issue since August. He said after the pair of shootings that he would resume pushing Manchin-Toomey, the background-check bill he became known for after the 2012 Sandy Hook Elementary School shooting.

Senate Republicans are looking for signals and political cover, from the president, but it’s still not clear what, if anything, Trump will support. Trump has in the past indicated he was interested in discussing background checks, but at other times has downplayed the idea.

Senate Majority Leader Mitch McConnell (R., Ky.) has said he won’t bring a gun bill up for a vote unless Trump says he’ll sign it. Meanwhile, House Democrats who passed a stricter background-check bill in February have sharply criticized Senate Republicans for refusing to bring that proposal for a vote.

The NRA called Barr’s proposal a nonstarter, Politico reported Wednesday, and the attorney general’s idea did not generate any new support from Republicans.

Toomey said his colleagues would continue waiting to see if a consensus emerges with the president. Though the attorney general’s proposal is “still in the idea stage," he said it would achieve the Manchin-Toomey bill’s goal of expanding background checks.

“It’s a constructive, thoughtful way that we can absolutely minimize inconvenience to law-abiding citizens and at the same time increase the chances that we can keep guns out of the hands of dangerous people," Toomey said.

That could mean expanding who is authorized to perform background checks beyond licensed firearms dealers — for instance, to law enforcement officers or justices of the peace — so that people in rural areas wouldn’t have to travel as far for background checks, Toomey said.

The proposal would also seek to quell concerns that a more robust background-check system would lead to a national firearms registry, Toomey said. Politico reported Wednesday that that may mean only one party keeps a record of a transaction.

Staff writer Jonathan Tamari contributed to this article.