ALBANY — Mayor Bloomberg and Governor Spitzer may get along fine when they run into each other in their Upper East Side neighborhood, but a month into the governor’s first term they are already clashing over budget numbers.

Yesterday, Mr. Bloomberg harshly criticized Mr. Spitzer’s budget proposal, saying it would blow “an enormous hole” in the city budget presented less than two weeks ago.

Mr. Bloomberg said the state in the past has attempted to “nickel and dime” the city by cutting the aid known as revenue sharing, but he said Mr. Spitzer is the first to push for its complete termination.

“If we lose these revenue-sharing funds now, does anybody seriously believe that we will ever get them back?” Mr. Bloomberg asked at a joint Senate and Assembly hearing in the state capital. “Something that’s gone is gone. Just take a look at the commuter tax.”

While Mr. Bloomberg praised Mr. Spitzer’s push to shake up the status quo in Albany, the mayor’s testimony made clear that he will not shy away from public conflict with the new governor. Given that Mr. Spitzer has repeatedly cited the mandate of his landslide election to restructure the state finances, the clash of these two New York titans is not surprising.

The budget is the first true test of the neighborly relationship that Messrs. Bloomberg and Spitzer share.

“Change is good,” Mr. Bloomberg said, referring to the new governor at a lunch after his testimony. “Eliot lives about three doors from where I live, so I can always have somebody give him a parking ticket if he doesn’t treat us well.”

Mr. Bloomberg cast the proposed cut to state aid, which would come to a combined $660 for this and next fiscal year, as fundamentally unfair and nonsensical. New York City, he argued, is carrying the state economy on its shoulders and thus should get more resources from the state.

The mayor said he was trying to ensure that Mr. Spitzer’s budget doesn’t “kill the golden goose.”

“At the very lease that means the state budget should not undercut New York City’s economy, which this budget does,” he said.

Mr. Spitzer’s office says that even with the cut, the city is coming out $1.4 billion ahead in the governor’s $120.6 billion budget for the next fiscal year.

Yesterday, the governor was attempting to build momentum for his proposals, as he appeared with education advocates who back his spending plan.

“I wouldn’t expect anyone to come to Albany … and say this is wonderful,” the Associated Press quoted Mr. Spitzer as saying. “When you look at the net, the city of New York comes out extraordinarily well.”

The largest chunk of the increase in state funding to New York City is $637 million for education — an amount that will grow to more than $3 billion in the next four years. The budget also proposes giving the city the $374 million it plans to collect from closing a slew of complicated tax loopholes. State budget officials say that will offset the cut to the revenue sharing money.

Mr. Bloomberg, however, argued that closing the loopholes is not an adequate substitute for the cuts. He pointed out that clamping down on those provisions could “take money out of our economy” — by more heavily burdening business owners.

Mr. Spitzer’s budget director, Paul Francis, downplayed the idea that budget has created any kind of rift, saying that the mayor and governor are in agreement on the largest aspects of spending.

“I don’t view it as a clash. On the most significant provisions of the budget, we have strong support from the mayor,” he said during a telephone interview, citing health care and education funding.

“We can’t be looking at the glass as 2% empty,” Mr. Francis said. “The glass is overwhelming full here.”

Nonetheless, the revenue sharing was not the only item Mr. Bloomberg took aim at yesterday. He also criticized Mr. Spitzer’s budget for “shortchanging” the city on property tax relief and for hiking the fees by $30 million for administering the city’s personal income tax.

He called the latter an “outrageous” move and said the city would propose legislation to authorize its own Department of Finance to take over the job itself.

Mr. Bloomberg’s criticisms of the budget were all focused on policy and were woven in with praise for Mr. Spitzer on a laundry list of proposals, including lifting the cap on the number of allowable charter schools, expanding health insurance for children, and increasing funding to hospitals that serve large Medicaid populations.

Both lawmakers have said that disagreements should be expected, given the sometimes-competing interests of the state and the city in the budget. Mr. Spitzer, for example, campaigned on a promise to jumpstart the upstate economy, while Mr. Bloomberg’s job is to boost the city.

Mr. Bloomberg took some criticism himself yesterday, from legislators who lashed out at his education policy. State Senator Ruben Diaz said the mayor’s top two education chiefs — Schools Chancellor Joel Klein and Deputy Mayor Dennis Walcott — should resign. Mr. Bloomberg dismissed that idea.

State Senator Bill Perkins of Harlem said that while the mayor was diplomatic when criticizing the governor yesterday, they have clear differences. “The gloves will be taken off,” he said. “The diplomacy will recede and bare-knuckle discussions will take place.”