WASHINGTON — The health-care bill unveiled yesterday restored to New York billions of dollars in federal payments that would have been cut in the Senate’s original version.

The bill reworked measures that would have cut $1 billion a year in Medicaid reimbursements to the state and about $1 billion a year in Medicaid payments to hospitals.

Mayor Bloomberg and Gov. Paterson had been complaining for weeks about shortchanging.

“From the early days of Senator [Daniel Patrick] Moynihan, New York has fought for the federal government to contribute more to our Medicaid program, as it does in many poorer states. We have finally achieved this in a very large way,” said Sen. Chuck Schumer (D-NY).

New York currently covers more people under Medicaid than most states and is reimbursed for 50 percent of its costs.

In the original Senate bill, states that expanded their Medicaid programs would be reimbursed for 93 percent of costs — a provision that would have excluded New York, which is now included.