WASHINGTON - Gov. David A. Paterson, beset by a state budget bleeding red ink, pressed Sen. Charles Schumer (D-N.Y.) again Tuesday to seek a higher level of federal funding to help pay for the Medicaid expansion in the Senate's bill for a health system overhaul.

In a letter to Schumer and Sen. Kirsten Gillibrand Tuesday, Paterson and New York City Mayor Michael Bloomberg warned that the bill's Medicaid policies could cost the state "close to $1 billion" a year.

Schumer aides disputed that calculation, saying the bill gives extra federal money to New York to help pay for the Medicaid expansion.

Paterson and Schumer have been jousting over that calculation for the past few months. At issue is whether New York is being penalized for already being "generous" on Medicaid.

Most states cover adults up to 100 percent of the poverty line, but New York covers parents up to 133 percent.

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The Senate bill would make all states offer Medicaid to adults at up to 133 percent of the poverty line. It gives states going only to the 100 percent level extra federal money to help pay for new beneficiaries.

However, the bill also gives New York and other states already offering expanded Medicaid new funds, but at lower levels, Schumer aides said.

Schumer spokesman Brian Fallon said the bill addresses issues of higher insurance premiums and Medicare going broke.

Schumer, he added, is "fighting to make sure New York is fairly treated in the bill."

"In many ways, such as medical education, the bill greatly benefits New York," Fallon said. "In some ways it could be better and he is fighting to make it better."