Senator Mitch McConnell of Kentucky, the majority leader, said on Sunday that he would be willing to bring a bipartisan proposal to stabilize health insurance markets up for debate if President Trump signaled his support.

“If there’s a need for some kind of interim step here to stabilize the market, we need a bill the president will actually sign,” Mr. McConnell said on CNN’s “State of the Union.” “And I’m not certain yet what the president is looking for here, but I’ll be happy to bring a bill to the floor if I know President Trump would sign it.”

Mr. McConnell’s comments shift attention to Mr. Trump, who has sent mixed signals about a proposal unveiled last week by Senators Lamar Alexander, Republican of Tennessee, and Patty Murray, Democrat of Washington. The president has left enough of an opening for the plan to proceed tentatively.

The proposal would extend federal payments to insurance companies through 2019 to reimburse discounts that the companies are required to provide to millions of low-income people who have coverage under the Affordable Care Act. Mr. Trump, who says that repealing President Barack Obama’s signature health law remains a top priority, had announced this month that he was cutting off those subsidies.