An uneasy truce between Governor Spitzer and Mayor Bloomberg is degenerating into a public quarrel over spending plans, with each side pointing fingers regarding who or what is to blame for the city’s financial straits.

Warning of a hit from the state, the city told agency heads that they have two weeks to identify ways to trim their budgets by another 3% next year, on top of cuts already in place for the coming year.

“The governor’s budget, as proposed, would cut roughly $700 million out of aid from Albany, which is really our money we’re sending up there,” Mr. Bloomberg said yesterday at City Hall. “That will put another hole in our budget.”

In a memo sent to agency heads, the city’s budget director, Mark Page, said the state’s executive budget proposal would cause “serious damage to our ongoing ability to provide vital services” if it were not substantially revised.

Testifying before the City Council’s Finance Committee, he implied that even more significant cuts could be on the way, saying that the new wave of potential reductions, which he projected would bring in more than $500 million, would not provide enough cover “for the threatened direct hit from the state.”

“I am extremely worried about the state and I’m not too happy about the economy,” he said. He added that he thinks the 3% cuts are “very likely going to be necessary in order for us to manage our way through the future.” The city says the state owes it about $747 million.

The state’s budget director, Laura Anglin, said in a statement that Mr. Page’s testimony to the council was “inaccurate and highly misleading.”

“He is attempting to shift the blame for the City’s budget cuts from where it rightly belongs: the economic downturn that is affecting every level of government,” she said. Mr. Spitzer’s budget provides a net positive impact on the city of nearly $671 million in 2009, and includes more funding for the city’s schools, she added.

The dispute over the city’s budget is the latest source of tension between Messrs. Bloomberg and Spitzer, who, while not close, have maintained cordial relations. Recently, however, the mayor’s support for the governor’s most powerful legislative opponents has created divisions between the two leaders.

A source close to the governor said administration officials were infuriated by a $500,000 donation to Senate Republicans made by the mayor. Mr. Bloomberg said he gave the money to reward the Republicans for standing behind his initiatives.

Spitzer administration officials are privately accusing the mayor of meddling in Albany politics at a time when the governor is close to overthrowing the Republican majority.

Despite the cuts, Mr. Bloomberg said the city would strive to maintain a $400 property tax rebate already in the budget, and uphold a 7% reduction in the property tax rate. The mayor warned that the tax cuts could be re-evaluated if the city’s fiscal outlook worsens.

“We have a long time between now and our budget adoption, we’ll see what happens to the economy,” the mayor said. “But before we even think about increasing the revenue side, we’re going to work on the expense side.”

Mr. Bloomberg noted that the city still enjoyed several advantages in weathering a widely predicted recession. He described the weak dollar as “a godsend for us,” in that it encourages tourism to the city. The mayor also cited low crime rates as a positive asset, saying the relative safety encourages people to live and invest in the city.

Council Member Lewis Fidler, who represents parts of Brooklyn, proposed that the city raise its hotel tax to bring in more revenue without taxing city residents. Last year, a record-breaking 46 million tourists were estimated to have visited New York City, pumping a projected $28 billion into the economy.

Council Member Peter Vallone Jr., who represents parts of Queens, offered up another solution to the city’s financial woes: secession from the state.

“All of our terms will be up soon and we will have made no difference when it comes to the imbalance that exists, when it comes to us getting the shaft from Albany,” Mr. Vallone said. “And we can continue these therapy sessions where we all sit around and get our anger out and we all yell and scream, or we can take the only action which is left to us and that is to seriously start a discussion of secession.”

The mayor has said the city’s taxpayers pay the state about $11 billion a year more than they get back.

The cuts to city agencies Mr. Bloomberg proposed in January are triggering the most vocal backlash from teachers, parents, and students, who are saying children and classrooms should be spared from the cuts.

A council member who is chairman of the Education Committee, Robert Jackson, said he estimated that in addition to another $200 million he says the schools are owed by the state, a further cut of 3% to the Department of Education’s budget would mean schools are facing about $1 billion in cuts. The city already had called for $180 million in cuts this year and another $324 million next year.

“I don’t believe our education system can absorb that,” he said.

Before the proposed reductions were announced yesterday, the city’s teachers union, the United Federation of Teachers, had planned a protest the cuts at City Hall on March 19 along with education and parent groups, union members, and elected officials, operating together under the title: “Keep the Promises Coalition.”

That group issued a report yesterday detailing the impact of the mid-year cuts on schools. The report said that in a survey of 375 schools, nearly half had cut orders for textbooks and instructional supplies; 48% cut after-school programs, weekend classes, and tutoring services; 36% were cutting back on student clubs and extracurricular activities, and 23% cut back on teacher training and professional development programs.

A spokeswoman for the Department of Education, Debra Wexler, said in a statement that no one wants to cut money from school budgets, but said the economy is struggling, revenues are down, and the city can’t afford to spend money it doesn’t have.

She said the department would have to wait until “Albany finalizes the State budgets before making any final decisions, but we obviously will look closely at Central and school budgets to implement cuts with the smallest possible impact on our students and schools.”