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 on 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 H.M.O.s, 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 Federal District Court in Los Angeles.