The Obama administration proposed rules Thursday for using the influential Medicare program to spur a controversial form of managed care emerging around the country that nudges doctors and hospitals to save money by coordinating treatment for their patients.

The rules are designed to carry out the first broad changes in the delivery of care under the year-old federal law intended to overhaul the nation’s health-care system.

The proposal lays out a path for hospitals, doctors and other care providers to form teams called accountable care organizations (ACOs) that can become responsible for all the medical needs of a group of older Americans on Medicare. Under the rules, the government will give monetary rewards to teams that treat patients for less money and demonstrate their quality.

In issuing the intricate proposal after months of delays, Health and Human Services officials predicted that such ACOs will save the financially strained program $510 million to $960 million during the first three years after they take effect in January. Critics, including insurers, warn that the arrangements could backfire by fostering large, powerful organizations of doctors or hospitals that could command higher prices by suppressing competition.

Nearly two decades after health-maintenance organizations began to proliferate across the U.S. health-care landscape — eventually becoming widely reviled — the law’s encouragement of ACOs represents a next generation of thinking.

While HMOs are run by insurance companies, ACOs are run by doctors and hospitals. Many health-policy experts think the nation’s soaring medical spending can be controlled by integrating all the care a patient receives, placing a greater emphasis on preventive services, and lessening expensive hospital readmissions and wasteful duplication of tests and other services.

Donald M. Berwick, administrator of the Health and Human Services Department’s Centers for Medicare and Medicaid Services, praised ACOs as an “exciting and productive” way to overcome the fragmentation of care for older patients. He noted that the typical Medicare patient has five chronic medical problems and sometimes is treated by a different doctor for each one.

The Medicare Shared Savings Program, as the law’s ACO provision is known, carries big stakes for doctors, hospitals, other caregivers and the insurance industry, as well as for older patients. The proposed rules are likely to spur a torrent of reaction. The government will provide a two-month window for public comment and is likely to adjust the rules before they are put into a final form, scheduled for later this year.

Unlike in Medicare Advantage, the managed-care part of Medicare, patients will not sign up for an ACO. Instead, they will be assigned to one at the end of each year if the doctor they see most often for primary care is part of such a group. Doctors who participate in an ACO must post signs and tell their patients.

However, the immediate response from various corners of the health-care system was scant, as the often-noisy factions in major health-care debates spent Thursday mired in the complex proposal’s 429 pages.

To be approved as an ACO, groups of doctors or combinations of doctors and hospitals must demonstrate that they are able to provide primary care for at least 5,000 patients. The rules also attempt to address concerns about organizations so big that they can leverage high prices. For instance, plans with more than 50 percent of the patients in a given market would need to prove to federal regulators that they do not run afoul of antitrust requirements.

To stimulate the formation of ACOs, newer organizations can be shielded from any downside risk for the first two years. Organizations that already are well-developed will, from the first year, save or lose money depending on whether they can provide care for a cost lower than the traditional Medicare fee-for-service rates.

The rules also define 65 standards by which quality will be judged. They fall into five areas: patients’ experiences in receiving care, the extent to which care is coordinated, patients’ safety, the degree of emphasis on preventive health, and the teams’ effectiveness in treating Medicare patients who are sick and frail. An ACO will reap savings only if it meets enough of the quality requirements.

Berwick said it is unclear how common ACOs will become in Medicare.