UnitedHealth Group, one of the nation’s largest health insurers, is accused in a scheme that allowed its subsidiaries and other insurers to improperly overcharge Medicare by “hundreds of millions — and likely billions — of dollars,” according to a lawsuit made public Thursday at the Justice Department’s request.

The accusations center on Medicare Advantage, a program through which people 65 or older agree to join private health maintenance organizations, or HMOs, whose costs the government reimburses.

The program was created in 2003 after UnitedHealth and other insurers said that managed care could help contain the overall cost of Medicare, which has strained the federal budget by rising faster than the rate of inflation.

Instead of slowing Medicare costs, UnitedHealth may have improperly added excess costs in the billions of dollars over more than a decade, according to the lawsuit, which was unsealed in U.S. District Court in Los Angeles.

A spokesman for UnitedHealth disputed that assertion, saying it was based on faulty interpretations of Medicare rules.

“We reject these more than five-year-old claims and will contest them vigorously,” said the spokesman, Matthew A. Burns.

Insurers and the federal government have been at odds for years over how private plans bill Medicare. A number of UnitedHealth companies sued the Health and Human Services Department last year, challenging proposed rules for how companies should handle overpayments by Medicare.

At the same time, whistle-blowers have filed lawsuits against insurers, claiming they overcharged the programs, and government audits have uncovered a widespread problem with private plans overcharging Medicare over a number of years.

The Justice Department’s court notice that it was joining the case involving UnitedHeath was filed by Chad Readler, a lawyer who joined the agency’s civil division as part of the Trump administration. It is intervening in the whistle-blower’s claims about erroneous coding and inflated billing but is not taking part in other claims.

The newly public accusations were first made in 2011, when a former UnitedHealth executive, Benjamin Poehling, filed a complaint under the False Claims Act, a federal law that allows private citizens to take legal action when they believe a government program has been defrauded.

Poehling’s complaint, which was among the documents unsealed Thursday, named 15 companies as defendants. Of those, the Justice Department told the court it wanted to intervene in the cases involving two, UnitedHealth and WellMed Medical Management, which UnitedHealth acquired in 2011.

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