Dr. Ludwig said other government programs had common-sense restrictions. The Special Supplemental Nutrition Program for Women, Infants and Children, better known as WIC, and the national school lunch program have strict nutrition standards. Medicare pays for necessary medical procedures but does not reimburse for ones it considers harmful, ineffective or unnecessary. SNAP, Dr. Ludwig said, should be structured similarly.

“No one is suggesting poor people can’t choose what they want to eat,” he said. “But we’re saying let’s not use government benefits to pay for foods that are demonstrably going to undermine public health.”

The federal government provides SNAP benefits to roughly 23 million households each month, many of them single-parent homes at or below the poverty line. The average household receives about $256 in monthly benefits. That means a household that spent 10 percent of its SNAP money on sweetened beverages could buy at least 20 two-liter bottles of orange Crush soda at a Fine Fare supermarket in New York City, or about 50 cans of Sprite at a Walmart near Oakland, Calif.

Since 2004, a number of cities and states have sought to restrict sugary drinks from their SNAP programs, including Maine, Minnesota and New York City under Mayor Michael R. Bloomberg in 2011. But doing so requires permission from the U.S.D.A., and the agency has denied every official request.

Mr. Concannon at the U.S.D.A. said the agency had “intermittent dialogue” with municipalities across the country about prohibiting the purchase of sugary drinks through SNAP. But he said the agency would grant a state or city permission to do so only on the condition that it first conducted “a rigorous pilot study” and offered food stamp recipients the ability to opt out of the soda restrictions.

“We’d want rigorous evaluation to see what is the impact of such a policy,” he said.

PepsiCo lobbied the federal government to prevent restrictions on food stamp purchases in 2011, 2012 and 2013, according to the Center for Responsive Politics, a nonprofit that tracks money in politics. Coca-Cola, Kraft Foods and the sugar industry lobbied against a Florida bill in 2012 that would have banned using food stamps to buy soda and junk food. And in 2011, the Snack Food Association teamed up with beverage industry lobbyists and the National Confectioners Association, which represents candy companies, to defeat New York City’s proposed ban on using food stamps to buy sugar-sweetened beverages.

Mr. Concannon said the U.S.D.A., rather than restricting junk foods, had made incentive programs that encourage nutritious foods a priority. The federal farm bill that designates money for the SNAP program, for example, set aside $100 million for programs that increase the value of food stamps that are used to buy fruits and vegetables at retail stores or farmers’ markets.