NEW YORK — A front in the national health care battle has opened in New York City, where a major hospital chain and one of the nation’s largest insurance companies are locked in a struggle over control of treatment and costs that could have broad ramifications for millions of people with private health insurance.

The fight is between Continuum Health Partners, a consortium of five New York hospitals, including Beth Israel Medical Center and St. Luke’s-Roosevelt Hospital Center, both major teaching hospitals, and UnitedHealthcare, which includes Oxford health plans and has 25 million members across the country, 1 million of them in New York.

While Congress has been haggling over covering as many as 15 million uninsured Americans, the prestigious hospitals and the major health insurer have been in bitter contract negotiations, not just over rates but also over UnitedHealthcare’s demand that the hospitals notify the insurance company within 24 hours after a patient’s admission. If a hospital failed to do so, UnitedHealthcare would cut its reimbursements for the patient by half.

UnitedHealthcare says the proposed rule is meant to improve the quality of care and cut costs by allowing insurance case managers to jump in right away. The hospitals say that having their reimbursement cut in half is too much to pay for a clerical error, and that the drain on their revenues would ultimately hurt their patients.

UnitedHealthcare is negotiating or imposing similar rules at hospitals across the country, and often meeting fierce opposition. Tennessee passed a law saying the penalty would not apply on weekends or federal holidays, when hospitals are short-staffed. Florida hospital officials said that the new rule could play a role in coming contract negotiations there, and that the state hospital association had asked Florida’s insurance regulators to monitor the situation.

The dispute signals a “ratcheting up” of a long tradition of insurers trying to cut costs, said Jeffrey Rubin, an economics professor at Rutgers University.

But Rubin said UnitedHealthcare’s approach is particularly aggressive and may be part of a wave of pressure insurance companies feel from employers to cut costs and to keep premiums lower to avoid penalties, like the “Cadillac tax” on expensive insurance plans.

Disputes between insurers and providers have flared up before, and it is rare for them to ultimately part ways. But the negotiations in New York have become especially tense. UnitedHealthcare has sent letters over the last few weeks to tens of thousands of patients, warning that they could be cut off from coverage at Continuum hospitals and affiliated doctors, and advising them to start shopping for new ones. Last year, 85,000 UnitedHealthcare customers received treatment from Continuum.

The hospital system went to court and got an injunction preventing the insurance company from cutting access to Continuum doctors until the matter could be arbitrated. And the Greater New York Hospital Association, a trade group, has complained to the state attorney general that the 50 percent penalty would be “confiscatory.” The attorney general’s office said it was reviewing the matter.

Health care analysts say that such battles could become more common if federal policy promotes competition among insurance companies, perhaps including insurance exchanges, as an important engine for driving down health care costs.

The fate of health care reform in Congress is unclear now that Democrats have lost their filibuster-proof majority in the Senate. The House and Senate have not reconciled their disparate bills, but both proposals would prevent health insurers from excluding people with pre-existing conditions, which is one way they hold down costs.

So the insurers will need to find other ways to control expenses, said Sean Cavanaugh, an analyst for the United Hospital Fund, a New York-based research institute. “That means you try to negotiate price reductions and control utilization, which is the hardest way for insurers to hold down costs,” he said.

UnitedHealthcare has been rolling out a similar policy across the country since 2007, but has repeatedly postponed deadlines and penalties in the face of opposition. Most recently, it postponed a Jan. 19 deadline to begin imposing the 50 percent penalty. (UnitedHealthcare documents suggest that in some cases, the full penalty would kick in only after 72 hours, but Continuum officials say that UnitedHealthcare is forcing them to negotiate such terms.)

Integris Health, an 11-hospital system based in Oklahoma City, has tried to meet the notification requirement and has been frustrated by the administrative burden, even using electronic notification, said Greg Meyers, vice president for revenue integrity. “That doesn’t feel to us like cost control. It feels like a revenue stream enhancement to the insurance companies,” Meyers said.

Continuum officials say that cutting reimbursement in half would mean the loss of at least $25,000 for a patient who had bypass surgery and $15,000 to $20,000 for elective joint replacement.

Dr. Gary Burke, a doctor affiliated with St. Luke’s-Roosevelt Hospital Center, said the letters warning that coverage with Continuum doctors could be cut off left some of his older patients panicked at the prospect of losing a long-term relationship with a doctor they trusted.

“They’re kind of like, ‘If I get sick, does this mean I can’t see you?’” Burke said.