As the clock winds down on Mayor Bloomberg’s final term, activists are pressing him to add another anti-tobacco initiative to his public health legacy: a cigarette tax hike.

Advocates for the tax increase say higher price tags on tobacco products deter would-be smokers and reduce the number of cigarettes purchased.

A vice president of advocacy for the American Cancer Society, Peter Slocum, said his organization is pressing the mayor to put the cigarette tax hike on his Albany agenda for 2008.

“We are aware of the clock,” he said. “Our goal is to try to raise the city and state excise taxes on tobacco before the mayor’s term expires.”

He said having Mr. Bloomberg in office has been an “almost once- in-a-lifetime opportunity” for public health advocates.

Mr. Bloomberg has said he supports raising the city’s cigarette tax by another 50 cents, but it is unclear how far he will go to back a push, given his attention to other legislative priorities, most notably a congestion-pricing proposal to charge drivers entering parts of Manhattan. The tax hike would need to be approved in Albany.

Under Mr. Bloomberg, the city’s cigarette tax was raised to $1.50, from 8 cents a pack in 2002, to bring it to a total of $3 when combined with a state tax on cigarettes.

The taxes have driven many New Yorkers — 27%, according to a recent study by the city’s Independent Budget Office — to buy their cigarettes out of state or from other sources.

Mr. Slocum said studies have shown that for every 10% increase in the price of cigarettes, there is a drop in overall consumption of about 4% and a drop in underage smoking of about 7%.

The city found that after it raised the cigarette tax in 2002, the proportion of New Yorkers who smoked dropped to 19.2% from 21.5%.

Mr. Bloomberg, who pushed through a ban on smoking in bars and restaurants during his first term, has not supported every anti-tobacco initiative. His administration criticized a proposed ban on the sale of flavored cigarettes, and he has threatened to veto bills that would have raised the minimum legal age to buy cigarettes.

He has not taken official positions on two pieces of smoking-related legislation recently introduced in the City Council: a proposal to ban smoking in cars in which minors are riding, and a proposal to prohibit smoking within 20 feet of a hospital entrance or on hospital grounds.

He has indicated that he is still focused on smoking issues by rolling out a new advertising campaign last month that focuses on the psychological barriers to quitting smoking.

A spokesman for M r . Bloomberg, Stuart Loeser, would not say how high a priority the cigarette tax hike would be for Mr. Bloomberg. He wrote in an email message that the city would deliver its preliminary budget in January, indicating that if Mr. Bloomberg were to try to raise the tax, it would be included in his budget.

The founder of Citizens Lobbying Against Smoker Harassment, Audrey Silk, said she is skeptical a cigarette tax hike would be approved in Albany, because the Senate majority leader, Joseph Bruno, has said he wouldn’t support it.

“They can push Bloomberg as hard as they want. As long as they have that barrier in the state, that’s a big factor,” she said.

A senior director of public policy and advocacy for the American Lung Association of the City of New York, Michael Seilback, said that in addition to the cigarette tax increase, he’d like to see more smoking-related legislation approved before Mr. Bloomberg leaves office.

“There are still fights left to fight,” he said. “We’re hoping that we can still see some success before those days tick away.”

The director of the New York City Coalition for a Smoke Free City, Joanne Koldare, said she doesn’t look at the end of Mr. Bloomberg’s term as a hard deadline.

“Our deadline is as soon as we can diplomatically work it out,” she said.

“Whether it’s Mayor Bloomberg or not, we all in tobacco control believe this is the next best thing to do.”