Mayor Michael R. Bloomberg’s $1.2 billion property tax increase won approval from the City Council on Thursday, raising homeowners’ bills by 7 percent as the city grapples with a worsening economy and disappearing revenue.

As a result of the 33-to-18 vote, annual tax bills will increase by hundreds or in some cases thousands of dollars, effective Jan 1.

“Even though it won’t be popular, New Yorkers will understand,” Councilman Miguel Martinez of Manhattan said in explaining his support for the tax hike. “Times are hard, and we’re asking everyone to pitch in.”

Opponents warned that residents were already overtaxed. Since Mr. Bloomberg took office, property taxes have increased by 18.5 percent.

“Today, the Council votes to take the bucket to the same old well and ask homeowners to bear the brunt of a swelling budget among dwindling revenues,” Councilman Simcha Felder of Brooklyn said. He added, “I believe that is unacceptable and that will hurt all New Yorkers in this difficult time.”

The property tax increase comes as Gov. David A. Paterson is pushing more than 100 new taxes and fees on items from downloaded music to nondiet sodas, and the Metropolitan Transportation Authority is moving to impose fare and toll increases.

Manhattan homeowners who live in the most expensive co-ops will see their taxes go up by anywhere from $854 to $1,307, according to the city’s Independent Budget Office. People who own single-family homes valued between $1 million and $1.5 million, outside of Manhattan, can expect to pay an extra $464 per year. Taxes on more modest homes, such as a condominium in Queens in the $300,000 to $400,000 range, would rise by $111.

To help ease the pain, Council Speaker Christine C. Quinn announced that Mr. Bloomberg had agreed to send homeowners the much-prized $400 rebate checks by the end of the calendar year.

The mayor had tried to eliminate the checks this year, then delay their distribution, but council members animatedly objected.

In addition, the Council approved an increase in the hotel tax from 5 percent to 5.875 percent per room, or about $3 a night. That change is expected to generate perhaps $80 million between March and the end of the next fiscal year, in June 2010.

Still, no one was under any illusions that the increased taxes would be the last financially difficult decision in the foreseeable future.

Mr. Bloomberg, who in September ordered all city agencies to cut spending by 5 percent, asked that they come up with an additional 7 percent in cuts by Dec. 22. And even with those cuts, and the extra revenue from higher taxes, the city is still facing a budget deficit of more than $1 billion in the next fiscal year.

The vote on Thursday — a close one by City Hall standards — was the latest political victory for Mr. Bloomberg.

He had unveiled his budget proposals just two weeks after the most bruising political battle in recent memory: the Council’s approval of his bid to rewrite the city’s term limits law, allowing him to seek a third term.

And his attempt to withhold the property tax rebate checks met with fierce condemnation from council members who portrayed Mr. Bloomberg, a billionaire many times over, as out of touch with the voters’ financial situation.

In recent days, though, with the help of Ms. Quinn, the Bloomberg administration began changing the minds of council members. It certainly did not hurt that the thrust of Mr. Bloomberg’s arguments was echoed when Governor Paterson presented his own bleak budget, filled with projected budget cuts in city funds. Nor did it hurt that the city comptroller, William C. Thompson Jr., a Democrat who is running for mayor, issued his own economic forecast this week.

Technically, Thursday’s vote repeals a tax cut of 7 percent that had been set to expire in June.

In a statement after Thursday’s vote, Mr. Bloomberg said: “It’s never popular to phase out a tax cut or reduce agency spending, but they are the right choices to avoid far greater and longer-lasting pain. We will not repeat the mistakes of the 1970s, which crippled city finances and nearly destroyed our quality of life.”

Councilman David I. Weprin of Queens said there were no plans, for now, to raise property taxes again in the next fiscal year.

“There is an unofficial agreement with the administration that they will not be coming back to us in June for an additional property tax increase,” he said. “Obviously, things could always change, but that was the general agreement as of now, by taking this tough vote midyear that we will not be asked to take another larger increase.”

The familiar dance between Mr. Bloomberg and the Council over the budget requires him to support some spending sought by the Council to win members’ backing. In this case, Ms. Quinn said that the Council was able to persuade Mr. Bloomberg to refrain from cutting approximately $20 million from a variety of programs, in exchange for adopting the Council&rsqu
o;s recommendations for $20 million worth of other cuts.

As a result, Mr. Bloomberg does not plan to cancel the next training class for more than 1,100 police cadets; instead, there will be two smaller classes of 250 cadets apiece in January and June.

In addition, the deal means that the mayor will not cut $2.5 million from City University of New York and community colleges for student services and research. Nor will he slice $3.7 million from the Administration for Children’s Services, which would have eliminated 127 caseworkers. Instead, Ms. Quinn said, the city will save $13 million by relying on in-house staff members and not consultants to do work on capital projects, as well as $3 million through a drop in fuel expenses.

There were also a few examples of city officials trying to make the additional taxes a little less onerous. Under a Bloomberg proposal, people who own properties valued at $250,000 or less can pay quarterly rather than semi-annually. Those people will also be given a 15-day grace period for payments due in January.