A $500 million hole has opened in Gov. Andrew M. Cuomo’s proposed state budget because of changes in how Washington plans to reimburse the state for the care of people with developmental disabilities, the governor said on Wednesday.

The state has been negotiating with the federal government for several months over the state’s billing practices; federal officials have said that the state has overbilled Medicaid for the institutional care of people with disabilities.

At a news briefing to announce changes to his proposed budget, the governor said, “The federal government takes the position the state has been overbilling, so to speak, for many, many years, going back over a decade, and the budget is going to be adjusted to reflect that new rate.”

To offset the new shortfall, Mr. Cuomo said that he was proposing that the state cut $120 million from the budget of the Office for People with Development Disabilities, and an additional $380 million from Medicaid programs.