As New Yorkers began digesting the city’s attempt to dissuade restaurants and food suppliers from using fat-laden vegetable oils, some said the move could leave the city vulnerable to lawsuits that might be hard to swallow.

On Wednesday, the Department of Health and Mental Hygiene announced a campaign to encourage restaurants and food suppliers to give up partially hydrogenated vegetable oil voluntarily. Hydrogenated oils contain trans fat, which is known to cause heart disease.

Lawyers said that while a negligence lawsuit against the city over trans fats would be difficult to prove, if public schools, jails, city senior centers, city hospitals, and other government-run facilities serve foods with trans fat, the warning could backfire.

A Manhattan personal-injury lawyer, Jeffrey Kimmel, said if city facilities serve foods with trans fat, a government advisory about trans fat’s dangers “could be some evidence of negligence.”

“It’s something that can be used to prove that they are doing something wrong,” he said. “Would it be an open-and-shut case? No. Would I take the case? No. But there may be a lawyer out there who would give it a shot.”

Officials at the Department of Correction, which runs Rikers’ Island and other city detention centers, did not respond yesterday to requests for information about their jails’ menus.

At the conservative think tank the Manhattan Institute, a senior fellow, Walter Olson, said he did not expect suits soon but would not be surprised if they eventually cropped up.

“There are lawyers sniffing around this area,” Mr. Olson said during a phone interview. “There are lawyers who have sued schools for having sugared sodas in vending machines.”

Officials at the Department of Education, which serves roughly 860,000 school meals daily during the school year, did not seem worried, though school cafeterias are not entirely rid of trans fats.

While they still serve some meat, french fries, and other processed items, the school system has been widely praised for replacing notoriously greasy foods with healthful alternatives. The executive director of the city’s School Food Program, David Berkowitz, said that last year the department phased in whole-wheat bread and next month when the school year starts all snack chips will be baked, whole milk will be replaced with 1% and 2%, and only cookies free of trans fat will be served.

The department, Mr. Berkowitz said, is also moving to baked french fries this year at all but about 30% of high schools. At those schools, the only ones left in the city with deep fryers, officials are looking for alternatives without hydrogenated oils. The hope is to be gin using alternatives in a few months.

“We’ve been very aggressive and we’ve gotten very good recognition for it, bringing in whole wheat, reducing sodium, pushing skim milk,” Mr. Berkowitz said. He said that the entire industry is retooling to accommodate new federal warnings about trans fat, but that there would be a lag time before the necessary adjustments can be made.

Officials at the city Department of Aging said the 329 seniors centers under their umbrella are not entirely rid of trans fat either, but that the meals they serve are all nutritionally sound. A department spokesman, Christopher Miller, said recent desserts have included sliced cantaloupe, Jell-O, strawberries, and apricots.

The city initiative has received praise from some public health officials, who said it appeared to be a creative way to tackle a serious health problem. And yesterday, the attorney who filed suit against McDonald’s on behalf of two overweight Bronx youths, Samuel Hirsch, told The New York Sun “anything that can eliminate trans fatty acids is good.”

Mayor Bloomberg and the city health commissioner, Dr. Thomas Frieden, have not backed away from health programs that advocates call progressive and critics call overly aggressive. Together they pushed for and won a controversial ban on smoking in many places, such as bars, where it had been permitted.

“The litigation side is probably not the first order affected by this,” the Manhattan Institute’s Mr. Olson said. “It is going to be a continuing area and we will hear more about trans fat. But the big problem is more that the city is acting like the worst kind of nanny toward its own citizens.”