WASHINGTON — In its quest to remake the nation’s health care system, the Obama administration has urged doctors and hospitals to band together to improve care and cut costs, using a model devised by researchers at Dartmouth College.

But Dartmouth itself, facing mounting financial losses in the federal program, has dropped out, raising questions about the future of the new entities known as accountable care organizations, created under the Affordable Care Act.

The entities are in the vanguard of efforts under the health law to move Medicare away from a disjointed fee-for-service system to a new model that rewards doctors who collaborate and coordinate care.

Medicare now has more than 400 accountable care organizations, serving eight million of the 57 million Medicare beneficiaries. Obama administration officials say the new entities are saving money while improving care, but some independent experts have questioned those claims.

“There’s little in the way of analysis or data about how A.C.O.s did in 2015,” said Dr. Ashish K. Jha, a professor at the Harvard School of Public Health. “The results have not been a home run.”

An evaluation for the federal government found that Dartmouth’s accountable care organization had reduced Medicare spending on hospital stays, medical procedures, imaging and tests. And it achieved goals for the quality of care. But it was still subject to financial penalties because it did not meet money-saving benchmarks set by federal officials.

“We were cutting costs and saving money and then paying a penalty on top of that,” said Dr. Robert A. Greene, an executive vice president of the Dartmouth-Hitchcock health system. “We would have loved to stay in the federal program, but it was just not sustainable.”

Dr. Elliott S. Fisher, the director of the Dartmouth Institute for Health Policy and Clinical Practice, said: “It’s hard to achieve savings if, like Dartmouth, you are a low-cost provider to begin with. I helped design the model of accountable care organizations. So it’s sad that we could not make it work here.”

Dr. Greene offered this analogy: It is easier for a person who runs a mile in 12 minutes to reduce the time to 10 minutes than for a five-minute miler to break the four-minute barrier.

Dartmouth-Hitchcock is the main teaching hospital for Dartmouth’s medical school, of which the Dartmouth Institute is part.

Since accountable care organizations began operation in 2012, a number like Dartmouth have dropped out of the program, citing financial uncertainties and unrealistic benchmarks for spending. Organizations with higher levels of prior spending had a greater ability to achieve cost savings in the first years of the program, by reducing unnecessary services, so they were more likely to qualify for financial rewards, according to the Government Accountability Office, an investigative arm of Congress.

The idea of accountable care organizations and the name are generally traced back to a paper in 2006 by Dr. Fisher and colleagues at Dartmouth and its medical school. Writing in the journal Health Affairs, they reported that Medicare beneficiaries received most of their care from doctors who were directly or indirectly affiliated with a local hospital.

In effect, this was an effort to overcome the fragmented nature of most American health care and to replicate some of the benefits of managed care while still allowing Medicare patients to visit any doctors they wanted.

The new entities, unlike health maintenance organizations, “can’t tell you which health care providers to see” and “can’t limit your Medicare benefits,” the Obama administration tells beneficiaries. But, it says, doctors and hospitals working together in an accountable care organization can share information, including test results and prescription drug data, so it is easier for them to coordinate care for patients.

Under the law, doctors and hospitals can share in savings if they meet certain goals established by Medicare officials, who set separate benchmarks for each group of health care providers.

Andrew M. Slavitt, the acting administrator of the federal Centers for Medicare and Medicaid Services, said that accountable care organizations were beginning to deliver tangible benefits. The current version is an early iteration “like the iPhone 2,” he said on Twitter.

Dr. Fisher said he was cautiously optimistic about the future of accountable care organizations. “Evidence on spending suggests modest savings over all,” he said, though he acknowledged that in Medicare “the model has yet to achieve the benefits many advocates hoped for.”

Accountable care organizations are one of many demonstration projects being conducted by the Center for Medicare and Medicaid Innovation, an office created by the Affordable Care Act to test new ways of financing and delivering care. Under the law, the secretary of health and human services has sweeping power to expand such projects nationwide if she finds that they would reduce Medicare spending without harming the quality of care.

The center is testing new ways to pay for prescription drugs, medical devices, cancer care, hip replacement surgery and many other services.

Republicans in Congress are taking aim at the center, saying its experiments jeopardize patients’ access to care and usurp the authority of Congress. In some cases, doctors and patients are required to participate.

“The agency has, in effect, enacted changes to the Medicare and Medicaid programs while circumventing Congress,” said Representative Tom Price, Republican of Georgia and chairman of the House Budget Committee.

The House Appropriations Committee has approved legislation that would eliminate $7 billion that remains available to the center.

Democrats defend the innovation center, saying the nation desperately needs to find ways of delivering better care at lower cost. To shut down the center or block its work would amount to “killing the baby in the nursery before it ever grows up,” said Representative Jim McDermott, Democrat of Washington.