While Democrats are still pushing for far-reaching legislation to restrict gun ownership, they’re also working with Republicans on more limited “red flag” laws to temporarily suspend Second Amendment rights of people deemed too dangerous.

Sen. Lindsey Graham, South Carolina Republican and new chairman of the Senate Judiciary Committee, has expressed interest, and lawmakers in both parties are pushing bills that would provide states with incentives to develop rules letting a family member or law enforcement officer petition a court to issue an “extreme risk” protective order.

“We’re beginning on a bipartisan basis,” said Sen. Jack Reed, a Rhode Island Democrat who is co-sponsoring one version introduced by Sen. Marco Rubio, Florida Republican. “It’s been adopted in several states so this is something that has bipartisan support. I hope we can build on the current support and get it through.”

Mr. Rubio’s home state is one of about a dozen states with “red flag” or “extreme risk” laws.

The measures gained renewed attention in the aftermath of last year’s school shooting at Marjory Stoneman Douglas High School in Parkland, Florida. Authorities admitted later that they missed warning signs that Nikolas Cruz, who has been charged with killing 17 students and educators, had a gun and wanted to hurt people.

The legislation from Mr. Rubio, Mr. Reed, Sen. Angus King, Maine independent, and Sen. Susan Collins, Maine Republican, creates a grant program within the Department of Justice to siphon cash to states that implement their own extreme risk laws.

Sen. Chris Murphy is also co-sponsoring red flag legislation but says he’d like to go further.

“If you pass legislation just giving incentives to adopt their own bills that’s a nice bill to pass, but that’s not going to save a whole lot of lives,” the Connecticut Democrat said. “If you created an actual federal protective order, that might be something substantial.”

Mr. Graham and Sen. Richard Blumenthal, Connecticut’s other Democratic senator, did roll out legislation after the Parkland shooting that would allow a family member or law enforcement official to petition a federal court to suspend the gun rights of dangerous individuals.

Mr. Graham says those discussions are continuing this year.

“There seems to be a lot that we actually agree upon, and I would like to make this a productive committee — bipartisan as possible,” said Mr. Graham, laying out his panel’s priorities earlier this month.

Sen. Joe Manchin III, West Virginia Democrat, said he’s also talked with Mr. Graham about the idea.

“I don’t know if it’s going anywhere, but it made a lot of sense,” he said.

While red flag processes vary somewhat, they generally give authorities a way to remove guns from the possession of someone without going through a full criminal proceeding.

In Florida, police can petition a judge to issue an order banning possession or purchase of a firearm. Hundreds of orders were issued in the first year of the law, with common reasons including domestic violence accusations, mental illness or suicidal tendencies.

The new process troubles gun rights advocates.

“Red flag laws are unconstitutional, as they destroy Due Process protections,” said Erich Pratt, executive director of Gun Owners of America.

Mr. Pratt said that even as eight states passed new protective order laws last year, his group helped to defeat them in nearly 20 states.

On Capitol Hill, red flag legislation will have to compete with other gun legislation.

The House Judiciary Committee advanced legislation earlier this month that would expand background checks to cover virtually all gun sales. Currently, only federally licensed dealers are required to perform the checks.

Some Democrats also want to use their new House majority to try to pass bans on military-style, semiautomatic rifles and high-capacity magazines.

Sen. Pat Toomey, a Pennsylvania Republican who tried to pass expanded background checks with Mr. Manchin after the 2012 Sandy Hook Elementary School shooting in Newtown, Connecticut, says he’d like to try that bill again, though he’s not sure there are 60 votes in the GOP-controlled Senate to break a potential filibuster.

He also shot down Democrats’ plans to try for bans on sales of some categories of weapons.

“I’m not interested in going beyond background checks. I’m not interested in banning categories of guns or other things that I think infringe on law-abiding” citizens, he said.

Yet Mr. Murphy said there could be pressure on some of the Republican senators up for re-election in 2020 to at least support the background check bill, which the full House is expected to take up as soon as next week.

“I’m always willing to try to find places to compromise, but this is crazy — universal background checks are supported by 97 percent of Americans,” he said. “This is political hari-kari for Republicans to continue to oppose it.”