A key Republican and Democrat in the Senate are attempting to find a bipartisan compromise on gun control legislation that would make it harder for people on the federal terror watch list to purchase firearms or explosives.

Senate Majority Whip John Cornyn, R-Texas, and Sen. Dianne Feinstein, D-Calif., are seeking a legislative middle ground between Cornyn's bill, which would impose a three-day delay for those on the list, and Feinstein's bill, which would ban people on the terror watch list from buying guns.

The two began negotiating after Senate Democrats halted floor action Wednesday with filibuster-like speeches advocating for Feinstein's bill and legislation expanding background checks to gun shows and the Internet. Democrats began pushing gun control measures this week following a terrorist shooting in Orlando on Sunday that killed 50 people and injured 53 others.

Both parties say they are willing to work on a deal that would close the so-called terror loophole that allows people on the terror watch list to purchase firearms.

"She approached him and they're talking," a GOP aide told the Washington Examiner, referring to Feinstein and Cornyn. "We all agree on stopping known or suspected terrorists from purchasing a weapon, the question is whether we do it in a way that's constitutional."

Both Democrats and Republicans said they are willing to work on a compromise, but the two measures include substantial differences.

Feinstein's legislation would place an outright ban on firearm purchases for those who appear on a federal terror watch list that includes those who are not permitted to fly.

Cornyn's legislation would place a 72-hour delay on gun purchases for people on the terror watch list, and it would require federal officials to prove in court that the person should not be allowed to buy guns.

Republicans oppose the Democratic bill because they believe it denies due process to those on the watch list, which is notoriously error-prone and includes many innocent people.

Democrats reject the GOP bill because it forces the government to show probable cause in order to block a gun purchase by someone on the watch list. Democrats say there would be no way for federal officials to vet every challenge, and that thousands of guns would wind up in the hands of people on the terror watch list.

The Senate's No. 3 Democrat, Chuck Schumer, D-N.Y., called Cornyn's bill "a meaningless compromise, a Pyrrhic victory and it's the kind of thing that all of us on our side of the aisle could not accept."

Sen. Pat Toomey, R-Pa., who in 2013 authored a bill that would have expanded background checks for gun purchases, joined Democrats on the Senate floor and called for a compromise.

Toomey said innocent people on the terror watch list would need a way to challenge the law if they are blocked from buying a gun. Feinstein's bill, Toomey said, "doesn't provide any meaningful opportunity" to challenge inclusion on the list.

But Toomey said Cornyn's bill may make it too difficult for federal officials to prove in court that a person should not be allowed to buy a gun. "There is an obvious opportunity here to work together to find a solution," Toomey said.

Republicans may be compelled to work out a deal with Democrats if they refuse to yield the floor and and instead continue the gun control filibuster.

Democrats have pledged to keep talking until a deal is reached on the terror loophole.

The filibuster was launched by Sen. Chris Murphy, D-Conn., who has been urging lawmakers to tighten gun control since the elementary school shooting in Newtown, Conn., which left 20 children dead.

"We've had enough of the condolences, the thoughts and prayers without action from this body," Murphy said.