WASHINGTON — Senate Republicans are closing in on a bill to repeal President Barack Obama’s signature health care law, diverging from the House on pre-existing medical conditions and maintaining federal subsidies that proponents see as essential to stabilizing insurance markets around the country.

The changes appear largely designed to appeal to Republican senators who hail from states where the Affordable Care Act is popular and who were critical of the House bill, which would eliminate insurance for millions of Americans covered under the current law, according to the Congressional Budget Office.

But the revisions may well alienate the Senate’s most conservative members, who are eager to rein in the growth of Medicaid and are unlikely to support a bill that does not roll back large components of the current law. Even with more moderate Republicans on board, party leaders would have a very narrow margin for passage on the Senate floor.

“I think it’s fair to say that the House bill was something necessary to move it to the Senate, but I don’t think that anyone expected that the House bill would define what the Senate did,” said Senator Bill Cassidy, Republican of Louisiana, who called the chances for approval in the Senate “better than 50-50.”