WASHINGTON — President Obama offered Tuesday to address some of the concerns expressed by Republicans in the health care debate as the two parties maneuvered for advantage heading into the legislative end game.

In a letter to Congressional leaders of both parties, Mr. Obama said he was open to four specific ideas raised by Republicans at the daylong health care forum last week, including encouraging the use of tax-advantaged medical savings accounts and increasing payments to doctors who treat Medicaid patients.

By signaling that he is open to the opposition’s ideas, Mr. Obama struck a bipartisan tone even as the White House prepared the ground for Democratic efforts to pass comprehensive legislation on a party-line vote. Mr. Obama is scheduled to speak about his strategy for passing the bill in remarks at the White House on Wednesday.

Democrats are planning to use a parliamentary device known as reconciliation that would allow them to complete the process with a simple majority vote in the Senate rather than subjecting the bill to the 60-vote requirement to overcome a filibuster. Republicans have denounced the use of the device on the health bill as short-cutting the regular process.

In response, the Senate minority leader, Mitch McConnell of Kentucky, warned that Republicans would use the health issue to bludgeon Democrats in this year’s midterm elections. If the Democrats “jam” an expansive bill through Congress, Mr. McConnell said, “it will be the issue in every single race in America this fall.”

In his letter, Mr. Obama said he was interested in four suggestions offered by Republicans at last week’s health care summit meeting, including an idea put forward by Senator Tom Coburn, Republican of Oklahoma, to have health care professionals pose as patients in undercover stings to root out fraud.

Mr. Obama also said he believed that high-deductible insurance policies, used in conjunction with health care savings accounts, could be offered to consumers in new federally regulated exchanges, or marketplaces, that would be created by his legislation.

The president said he also supported providing $50 million in grants to states to help them test alternatives to the current system of resolving medical malpractice claims. But Mr. Obama stopped far short of endorsing Republican proposals to impose hard limits on damage awards in medical malpractice lawsuits.

To answer Republican criticism of a proposed expansion of Medicaid, he said he agreed that it would be helpful to increase payment rates to doctors “in a fiscally responsible manner.”

But the president again rejected calls by Republicans for Democrats to discard the bills adopted by the House and Senate late last year and to start over with a step-by-step approach.

“Piecemeal reform is not the best way to effectively reduce premiums, end the exclusion of people with pre-existing conditions or offer Americans the security of knowing that they will never lose coverage, even if they lose or change jobs,” Mr. Obama wrote.

In the letter, he said Democrats and Republicans agreed about the need to fix the health care system, even if they disagreed on the remedies, and he seemed to be trying to build on the public display of bipartisanship at last week’s meeting and to blunt Republican criticism that Democrats are pursuing a partisan bill.

“My ideas have been informed by discussions with Republicans and Democrats, doctors and nurses, health care experts and everyday Americans — not just last Thursday, but over the course of a yearlong dialogue,” Mr. Obama wrote. “Both parties agree that the health care status quo is unsustainable. And both should agree that it’s just not an option to walk away.”

Republicans said they welcomed the president’s interest in their ideas, but said it was a meaningless gesture if Democrats remained intent on pushing through expansive, and expensive, legislation, which the Republicans assert would unwisely raise taxes and reduce federal spending on Medicare.

Mr. Coburn, in a statement, said Democratic leaders could continue to work with Republicans on areas of agreement — “or they can attempt an all-or-nothing reconciliation strategy based on the deeply flawed Senate and House bills and most likely accomplish nothing.”

Mr. McConnell, at a news conference, cited the Republican victory in the Massachusetts special Senate election in January as an example of what could happen to Democrats if they succeed in adopting sweeping health care legislation “over the objections of the American people.”

The bills passed by the House and the Senate would expand Medicaid to cover some 15 million people who are now uninsured. But in most states, payment rates are so low that many doctors do not accept Medicaid patients, a point that Senator Charles E. Grassley, Republican of Iowa, raised at the forum on Thursday.

“There’s no question Medicaid won’t be able to provide adequate access,” Mr. Grassley said in response to Mr. Obama’s letter. “It’s good if the White House has figured that out.”

Higher Medicaid payment rates could substantially raise the cost of the bill, even as Democratic leaders try to hold down the price tag to secure the support of fiscal conservatives in their own party.

As they begin a final push to round up votes, Democrats are also struggling to figure out how to orchestrate the intricate legislative maneuvers that will be needed to complete their bill.

Under the tentative plan, they said, the House would adopt the bill passed by the Senate on Dec. 24, and both chambers would approve a package of revisions in a separate budget reconciliation bill. The changes would bridge differences between the House and the Senate and incorporate some of Mr. Obama’s proposals.

Senator Kent Conrad, Democrat of North Dakota and chairman of the Budget Committee, said it might be possible to use the reconciliation procedure for “a set of relatively minor matters that have a budget impact.”

Coordinating the work of the two chambers could be “extraordinarily complicated,” he said.

In addition, the budget reconciliation process could be time-consuming in the Senate, where Republicans said they would raise procedural objections and offer numerous amendments.

Mr. Conrad said the budget bill might be used to “increase the affordability” of health insurance, by increasing subsidies for some people, and to increase federal payments to states for people newly eligible for Medicaid.

But to comply with reconciliation requirements, Mr. Conrad said, the budget bill would have to reduce the deficit over the next five years, taken together, and must not increase the deficit in any year thereafter.

The budget bill could probably not be used to establish restrictions on insurance coverage of abortion, an issue that deeply divides the House and the Senate, Mr. Conrad said.

Senator Olympia J. Snowe, Republican of Maine, said she was not impressed by the concessions Mr. Obama offered in his letter. “It’s always welcome, inserting Republican ideas,” Ms. Snowe said. “But it does not ameliorate other issues. The basic legislation is not going to change. That continues to be troubling.”