WASHINGTON — Two labor unions have pulled out of a broad coalition seeking agreement on major changes in the health care system.

The action, by the American Federation of State, County and Municipal Employees and the Service Employees International Union, shows the seeds of discord behind the optimistic talk at a White House conference on health care this week.

It also illustrates the difficulty of reaching agreement on two of the knottiest issues in the health care debate: whether to offer a new government-sponsored insurance option, and whether to require employers to help pay for employee health benefits.

Labor unions and leading Democrats in Congress support both ideas. But insurers and many employers oppose them.

The coalition, known as the Healthcare Reform Dialogue, is led by the president of the American Hospital Association, Richard J. Umbdenstock, and includes representatives of doctors and nurses, patients and consumers, insurers, drug companies and employers of all sizes.

Peter S. Adler, president of the Keystone Center, a nonprofit group facilitating the discussions, said the dialogue started with 20 participating organizations and now had 18.

“S.E.I.U. and Afscme have left the table,” Mr. Adler said Friday in an interview. “They have voluntarily pulled out at this moment. We are trying to keep the lines of communication open.”

Mr. Adler, a professional mediator with 30 years of experience, said the coalition had been meeting since September. It tentatively plans to issue recommendations later this month on how to rein in health costs and help achieve the goal of universal coverage. Congress is grappling with the same issues and is struggling to find bipartisan consensus.

Members of the dialogue said they had been unable to reach agreement on proposals for a new public insurance plan or a requirement for employers to contribute to the cost of coverage.

Steven Kreisberg, director of collective bargaining and health care policy at the federation of state, county and municipal employees, said: “I can confirm that we did drop out of the dialogue last week. We are no longer part of the group.”

Mr. Kreisberg said his union had withdrawn for “various reasons,” which he declined to discuss.

The federation has flooded Congress with petitions supporting affordable health care for all. The petitions say Americans should have “the choice of a public plan, so we’re not left at the mercy of the same private insurance companies that have gotten us into this mess.”

In the past, the federation has suggested that a public plan option could “build both public support and the infrastructure for a single-payer system” at some distant point in the future.

Insurance companies and many Republicans resist the idea of a new public plan, saying it would have unfair advantages and could ultimately drive some private insurers from the market.

One participant in the dialogue, speaking on condition of anonymity because the talks were supposed to be secret, said, “The final report will be a consensus product reflecting the lowest common denominator.”

Another participant, Ronald F. Pollack, executive director of Families USA, a liberal-leaning consumer group, said the two unions “wanted a more robust, expansive agreement.”

In the campaign, Mr. Obama proposed a public plan option and said he would require large employers to contribute to the cost of coverage for their employees or to the cost of the public plan.

Lori Lodes, a spokeswoman for the Service Employees International Union, said: “We support the public insurance option. We strongly support the health care proposal President Obama laid out in the campaign.”

Ms. Lodes declined to discuss her union’s relationship with the coalition. She referred questions to Mr. Adler, the mediator.

The most active participants in the coalition include Karen M. Ignagni, president of America’s Health Insurance Plans, a trade group, and Billy Tauzin, president of the Pharmaceutical Research and Manufacturers of America, which represents drug companies. Top executives from the American Medical Association, the Blue Cross and Blue Shield Association and the United States Chamber of Commerce have also been participating.

In a further effort to build consensus, the Obama administration announced on Friday that it would hold five regional forums on health care. They will be held in California, Iowa, Michigan, North Carolina and Vermont.