By Richard Cowan and Andy Sullivan
WASHINGTON (Reuters) -Democrats in the U.S. Senate said on Tuesday they were encouraged by talks with Republicans on firearms legislation, but warned that any compromise would fall well short of all the steps they say are needed to curb gun violence.
"Every day we get closer to an agreement, not farther away," said Senator Chris Murphy of Connecticut, who is working with Republican Senator John Cornyn of Texas on a possible deal.
The Senate's top Republican, Mitch McConnell, said he hoped the two sides would find common ground after a wave of mass shootings in Buffalo, New York; Uvalde, Texas; Tulsa, Oklahoma; and elsewhere.
"We're hoping to actually get an outcome that will make a difference," he said at a news conference.
Senate Democratic Leader Chuck Schumer of New York said he would give negotiators until at least the end of the week to reach a deal.
The talks have raised hopes of a rare bipartisan agreement on gun-related issues in Congress, which has failed to act after similar mass shootings over the past decade.
Most Americans support stronger gun laws, opinion polls show. Several relatives of those killed in recent shootings, as well as actor and Uvalde, Texas, native Matthew McConaughey, visited Washington on Tuesday to urge action.
"It's not about Republicans. It's not about Democrats. It's about people. It's about human life," said Kimberly Salter, whose husband, Aaron Salter Jr., was among the 10 people killed at a Buffalo supermarket.
Democratic President Joe Biden supports the effort, White House spokeswoman Karine Jean-Pierre said. "He is optimistic about what he's seeing," she said at a press briefing.
But any agreement that emerges will not likely include the new limits on gun ownership that Biden and most other Democrats say are needed to reduce gun violence that claimed more than 45,000 American lives last year.
Biden last week called for banning semi-automatic, assault-style rifles and high-capacity magazines, or at least raising the minimum age to buy those weapons from 18 to 21. The gunmen in the Buffalo and Uvalde shootings were both 18 and used semi-automatic rifles.
The Democratic-controlled House of Representatives is expected to approve some of those proposals on Wednesday, but they are unlikely to clear the evenly divided Senate, as many Republicans are opposed to tighter gun controls.
"Obviously, an agreement that we reach with the Republicans won't come close to the full list of things that I think are necessary to curb this epidemic," Murphy said. "But the Americans people are looking for progress."
Instead, Murphy and Cornyn are considering more modest proposals: encouraging states to adopt "red flag" laws to deny firearms to people deemed a risk to public safety or themselves; upgrades to school security; strengthening mental health services; and doing more to keep guns out of the hands of people who are legally barred from owning them, such as felons.
Senator Roy Blunt of Missouri told reporters that Cornyn got a positive reception from fellow Republicans during a closed-door briefing on the negotiations, but did not provide details on any of the measures that could be included.
The U.S. Supreme Court this month is expected to rule on a New York state case that could bring a sweeping expansion of gun rights.
Firearms ownership has been one of the most hotly contested issues in the United States. Gun rights advocates, including most elected Republicans, staunchly maintain that the Second Amendment of the U.S. Constitution guarantees the right to bear arms. Gun control supporters say permissive U.S. gun laws lead to needless deaths.
(Reporting by Richard Cowan, Andy Sullivan, Katharine Jackson and Rami Ayyub; Editing by Jonathan Oatis)