Congress debated but rejected restricting the purchase of sugared drinks with food stamps as part of a 2008 farm bill, Mr. Hacker said. But this year, the chairman of the House’s Agriculture Committee, Collin Peterson, Democrat of Minnesota, said the House should think about such a ban in its deliberations over the next farm bill.

Mr. Bloomberg and his health commissioner, Dr. Thomas A. Farley, said the ban would help curb the city’s obesity epidemic, which they contend has been fueled by rising soda consumption over the past 30 years.

City statistics released last month showed that nearly 40 percent of public-school children in kindergarten through eighth grade were overweight or obese, and that obesity rates were substantially higher in poor neighborhoods. City studies show that consumption of sugared beverages is consistently higher in those neighborhoods.

Dr. Farley and the state’s health commissioner, Dr. Richard F. Daines, said in an Op-Ed article in The New York Times on Thursday that the ban would not reduce the ability of food-stamp recipients to feed their families. “They would still receive every penny of support they now get, meaning they would have as much, if not more, to spend on nutritious food,” Dr. Farley and Dr. Daines wrote. “And they could still purchase soda if they choose — just not with taxpayer dollars.”

The health of New Yorkers, and particularly obesity, is one of the mayor’s signature issues. During his first term in office, Mr. Bloomberg expanded the city’s smoking ban to almost all indoor public places, and he is proposing to expand it to beaches, parks and plazas. New York City has banned trans fats in restaurants and requires restaurants to post calorie counts.

The city’s campaign against sugary drinks has been especially aggressive. This week, it introduced ads showing a man drinking packets of sugar. But its attempt to persuade the State Legislature to impose a tax on the drinks was met with skepticism and opposition from the beverage industry and grocery owners.

Tracey Halliday, a spokeswoman for the American Beverage Association, said of the mayor’s request: “This is just another attempt by government to tell New Yorkers what they should eat and drink.”