It is not clear what political dynamics might have changed since Friday, when a coalition of hard-line conservatives and more moderate Republicans torpedoed legislation to repeal President Barack Obama’s signature domestic achievement. The replacement bill would still leave 24 million more Americans without insurance after a decade, a major worry for moderate Republicans. It would also leave in place regulations on the health insurance industry that conservatives find anathema.
Mr. Ryan declined to say what might be in the next version of the Republicans’ repeal bill, nor would he sketch any schedule for action. But he said Congress needed to act because insurers were developing the premiums and benefit packages for health plans they would offer in 2018, with review by federal and state officials beginning soon.
The new talks, which have been going on quietly this week, involve Stephen K. Bannon, the president’s chief strategist, and members of the two Republican factions that helped sink the bill last week, the hard-right Freedom Caucus and the more centrist Tuesday Group.
Any deal would require overcoming significant differences about how to rework a law that covers about one-fifth of the American economy, differences that were so sharp they led Mr. Trump and Mr. Ryan to pull the bill from consideration just as the House was scheduled to vote on Friday.
Still, Republican members of Congress said they hoped that revisiting the issue would lead this time to a solution and a vote in the House.
“I think everyone wants to get to yes and support President Trump,” said Representative Dave Brat, Republican of Virginia and a Freedom Caucus member. “There is a package in there that is a win-win.”
Representative Raúl Labrador of Idaho, another Freedom Caucus member, said he hoped the discussions would yield a compromise that brings the party together after a divisive debate that revealed deep fissures. “I think we will have a better, stronger product that will unify the conference,” Mr. Labrador said.
Mr. Trump has sent mixed signals in recent days, at times blaming the Freedom Caucus, outside groups and even, it appeared, Mr. Ryan. On Monday, for instance, he said in a late-night Twitter post that the Freedom Caucus was able to “snatch defeat from the jaws of victory” over the health care repeal. “After so many bad years they were ready for a win!”
But then he suggested that he could also cut a deal with Democrats, a move that would almost certainly make more conservative members of the House balk. “Don’t worry,” he tweeted later Monday night, “we are in very good shape!”
Mr. Ryan said House Republicans were determined to use the next version of the repeal bill, like the first version, as a vehicle to cut off federal funds for Planned Parenthood clinics.
Asked if he saw any signs that members of the conservative House Freedom Caucus might be willing to compromise, he said: “I don’t want us to become a factionalized majority. I want us to become a unified majority, and that means we’re going to sit down and talk things out until we get there, and that’s exactly what we’re doing.”
“We saw good overtures from those members from different parts of our conference to get there because we all share these goals, and we’re just going to have to figure out how to get it done,” Mr. Ryan said.
Mr. Scalise said that “we’re going to keep working” because “this issue isn’t going away,” and he added: “Obamacare continues to fail the American people. You’re going to continue to see double-digit increases in premiums because Obamacare doesn’t work.”
Democrats took formal steps to get involved in what they called improving the Affordable Care Act. Representative Nancy Pelosi of California, the Democratic leader, sent a letter to House Democrats calling for suggestions in ways to make the health law work better. “We can then discuss these suggestions in our caucus and be prepared at the earliest possible time to go forward,” she said.