WASHINGTON — With Congress back in Washington from its six-week recess, the gun debate on Capitol Hill assumed a familiar shape Tuesday, with Democrats moving forward on legislation while Republicans huddled to determine what measures they — and, more critically, President Donald Trump — could swallow.

House Speaker Nancy Pelosi, D-Calif., and members of the congressional Gun Violence Protection Task Force held a forum Tuesday on Capitol Hill on gun violence legislation, amid a fresh push for action in the wake of mass shootings last month in Texas and Ohio.

In the afternoon, several House Democrats and Reps. Peter King, R-N.Y., and Brian Fitzpatrick, R-Pa., were expected to hold a press conference to call for Senate action on gun safety.

The House Judiciary Committee then began marking up measures to reduce gun violence Tuesday, a process likely to continue into Wednesday.

Meanwhile, top congressional Republicans from the House and Senate are expected to huddle with Trump at the White House Tuesday afternoon to discuss the fall legislative agenda, including potential legislation action on guns. Those expected to attend the meeting include Senate Majority Leader Mitch McConnell, R-Ky., Senate Assistant Leader John Thune, R-S.D., House Minority Leader Kevin McCarthy, R-Calif., and House Minority Whip Steve Scalise, R-La.

McConnell, for his part, said last week in an interview with radio host Hugh Hewitt that he expected to hear from the White House within a week what type of legislative response the president might accept on the issue. After the spate of mass shootings last month, Trump expressed some openness to stronger background checks, but then wavered following conversations with National Rifle Association leaders. His recent statements have focused more on proposals to address mental health

Speaking on the Senate floor Monday afternoon, McConnell laid out what the upper chamber plans to address this fall, which he said includes approving nominations and passing government funding. He made no mention of gun legislation.

“Leader McConnell did not even mention gun violence in his opening remarks today, after promising that we would have a debate in the Senate when we returned. We await word from the leader when that debate might take place,” Senate Minority Leader Chuck Schumer, D-N.Y., said on the Senate floor afterward. “One thing we do know is that Leader McConnell has said that the question of background checks will come down to President Trump. ‘If the president took a position on a bill,’ Leader McConnell said, ‘I’d be happy to put it on the floor.’ That’s what he said, those are his words.”

Thune, leaving a meeting of Senate Republican leadership Monday, confirmed the caucus was waiting for guidance from Trump. “I can say I think all of our members, at least if this meeting was any indication, believe that the president needs to indicate what it is he would be for....We’re obviously very interested in knowing what they are — what his plan or proposal is, and what he would be willing to sign.”

Democrats have been calling on McConnell to take up a bill the House passed in February that would expand background checks, but the White House issued a veto threat on the measure.

Some proposals that the White House is considering include a background checks bill pushed by Sens. Joe Manchin, D-W.Va., and Pat Toomey, R-Pa., a red flag bill, and a measure that would increase penalties for people buying a gun for someone else to circumvent background checks.

Vice President Mike Pence has also been pushing the idea of accelerating the death penalty for people who carry out a mass murder, though most mass shooters don’t survive the shootings. If such a provision is tied into a comprehensive gun package, that could be a deal-breaker for Democrats.

It remained unclear what measures rank-and-file Senate Republicans actually supported, if any — and which might they be willing to vote for. Asked Monday if the Senate should take up some kind of gun control measure, Sen. John Kennedy, R-La., told reporters that he's willing to talk about possible proposals, but sounded a cautious note on any potential action.

“Here's my starting point, I said it the other day: I do believe love is the answer, but I own a handgun just in case," Kennedy said, "I’m interested in facts and I want to see the causal scientific evidence [with gun restriction proposals]. Because we’re dealing with people’s constitutional rights."

Heading into a closed-door caucus meeting Tuesday morning, Pelosi gave a measured response when asked by reporters what her understanding is of where Trump stands on background checks.

“I’m hopeful, I'm prayerful,” she said.

In an interview with NBC News Monday, House Judiciary Committee Chairman Jerrold Nadler, D-N.Y., rejected the idea of a measure floated by White House officials that would only take guns away from those who are mentally ill.

"It is not an acceptable starting point," Nadler said.

"The president said after one of the mass shootings he will support background checks, then he spoke with the NRA and said he wouldn't," he added.

Toomey also sounded a cautious note on Tuesday.

"Look, I'm still hopeful. This is always difficult," he told reporters when asked if he was optimistic there might be some movement on the issue. "This was never going to be easy."

The Pennsylvania senator said he had spoken with the president "many times" about potential solutions. "The president is interested in doing something in this space, and I think the most sensible thing to do is some variation on Manchin-Toomey," he said. "I think the idea of having background checks on commercial gun sales makes all the sense in the world, and is very broadly supported. So I don't think there's any reason to give up yet, and I don't intend to."