Ratcheting up the pressure in a bitter battle between New York City and the state over health care costs, the city’s public hospital system is planning on suing New York State officials over a payment of some $380 million in federal funding it says the state is unlawfully withholding.

“You can’t just change the pattern of payment without approval of the federal government,” Dean Fuleihan, the city’s budget director, said on Friday, adding those payments “belong to Health & Hospitals.”

The disagreement stems from the delay of so-called Disproportionate Share Hospital payments, known as D.S.H., which are federal payments that help defray hospitals’ costs of caring for uninsured and poor patients.

In New York, those payments were typically handed out to NYC Health & Hospitals in the summer or early fall, according to Stanley Brezenoff, the interim president of the organization. This year, however, Mr. Brezenoff says his hospitals are owed $380 million for treating some 1.2 million patients, about one third of whom are uninsured.