ALBANY — Mayor Bloomberg is calling on state lawmakers to give the city $500 million he says it is owed in Governor Spitzer’s budget, and warning that without the restorations, the city will have to raise taxes or make deeper cuts. “We are not asking for anything other than our fair share,” Mr. Bloomberg said while testifying in Albany yesterday on the governor’s budget. “But our fair share is what we deserve.”

About one-third of the money Mr. Bloomberg says the city is due would have come in the form of a revenue-sharing grant. Last year, the city was supposed to receive no revenue-sharing money, but the state later set aside $20 million and promised to give the city its full share this year, the mayor said.

Now, he added, “We find that the instead of this promised full share, we’re budgeted to receive only half of what we’re due,” or about $164 million.

One of the centerpieces of Mr. Bloomberg’s $58.5 billion budget is a 7% property tax cut that would save New York City property owners about $1 billion next year. Despite expectations that he would urge lawmakers to help him keep the cut by sending more money downstate, he did not make a direct appeal during his testimony.

The mayor later told reporters that the fate of the tax cut is contingent not only on the state’s support, but also on help from the federal government, the health of the economy, and cooperation from municipal unions. He would not say whether the tax cut would be scrapped if the state did not give the city the funds it had been anticipating.

During his testimony, Mr. Bloomberg pressed lawmakers to allow the city to raise the tax on cigarettes by 50 cents, so that the total city and state tax on cigarettes would be $3.50.

“Make no mistake about it, if you don’t raise the tax, we are killing people,” he said.

He balked at Mr. Spitzer’s call for the city to pay the state $80 million next year for administering the city’s personal income tax, a $10 million increase, arguing that the fee should be going down because more New Yorkers are filing their income taxes electronically.

Mr. Bloomberg also hammered on the state for reneging on its commitment to support capital funding for school repairs, saying city taxpayers agreed to put $6.5 billion into school construction over five years and the state had promised to match that.

Taking a dig at Mr. Spitzer, the mayor also spoke to reporters about his distaste for governments’ reliance on revenues from gambling operations, saying it is a regressive way to raise money and that it is misleading to link gambling revenues, for instance, with education funding.

Mr. Spitzer is planning to lease the state lottery to a private company to generate billions of dollars for the endowments of the State University of New York and the City University of New York. The governor released a statement yesterday that said the economic downturn “demands fiscal restraint from leaders across the country” and argued that the city fared well in his budget, receiving a net increase of $1.2 billion over last year.

“I understand the City did not get everything it wanted but rocky economic times mean that every recipient of state funds must share the responsibility of across the board belt tightening,” he said.

He said state school aid to the city should increase to $8.2 billion next year from $7.6 billion and said the revenue-sharing money from the state would jump to $163.9 million from $20 million last year.

Mr. Bloomberg told reporters that he sympathized with Mr. Spitzer. Negotiating over the budget isn’t personal, he said.