If approved, it would be the first time an item would be banned from the federal program based solely on nutritional value.
The idea has been suggested before, including in 2008 in Maine, where it drew criticism from advocates for the poor who argued it unfairly singled out low-income people and risked scaring off potential needy recipients.
In 2004 the USDA rejected Minnesota's plan to ban junk food, including soda and candy, from food stamp purchases, saying it would violate the Food Stamp Act's definition of what is food and could create "confusion and embarrassment" at the register.
Some New Yorkers who receive the assistance said officials had good intentions but felt the proposal went too far.
"I can see the sodas, but suppose somebody's in bad shape and they just want juice?" said Harold Vilson, a 56-year-old Brooklyn resident who said he uses food stamps.
"If people want to buy that stuff, they should be able to. If it's not an illegal product, they should be able to buy what they want to buy."
The food stamp system, which was launched in the 1960s, serves some 40 million Americans a month and does not currently restrict any other foods based on nutrition. Recipients can essentially buy any food for the household, although there are some limits on hot or prepared foods.
Food stamps also cannot be used to buy alcohol, cigarettes or items such as pet food, vitamins or household goods.
The city and state proposal would be temporary, so officials could study its effects over two years. It would apply only to food stamp recipients in New York City - 1.7 million of the city's more than 8 million residents - and would not affect the amount of assistance they receive.
"This initiative will give New York families more money to spend on foods and drinks that provide real nourishment," said a statement from Bloomberg, who also has outlawed trans-fats in restaurant food and has forced chain restaurants to post calorie counts on menus.
In fiscal year 2009, New Yorkers received $2.7 billion in food stamp benefits and spent $75 million to $135 million of that on sugary drinks, the city said.
The ban would apply to any beverage that contains more than 10 calories per 8 ounces, except for milk products, milk substitutes like soy milk and rice milk, and fruit juices without added sugar.
A 20-ounce sugar-sweetened drink can contain the equivalent of as many as 16 packets of sugar.
Advocates for the poor expressed alarm Thursday about the proposal, which the New York City Coalition Against Hunger said "punishes poor people for the supposed crime of being poor."
"It's sending the message to low-income people that they are uniquely the only people in America who don't know how to take care of their family," said Joel Berg, the group's executive director. "The problem isn't that they're making poor choices, the problem is that they can't afford nutritious food."
There still are many unhealthful products New Yorkers could purchase with food stamps, including potato chips, ice cream and candy. But officials said the proposal targets sugary drinks because they are the largest contributor to obesity.
In New York, a proposal to adopt a penny-per-ounce tax on sweetened soda failed to get out of the state Legislature earlier this year; Bloomberg backed the state proposal.
"We continue to see a dramatic rise in obesity among children, especially in low-income communities," state Department of Health Commissioner Richard Daines said. "This initiative targets a major public health threat - the high consumption of sugary beverages - which have little to no nutritional value."
More than half of adult New York City residents are overweight or obese, along with nearly 40 percent of public school students in kindergarten through eighth grade.
City officials said lower-income residents are most likely to drink one or more sugar-sweetened drinks a day; type 2 diabetes is also twice as common among poor New Yorkers compared to the wealthiest.
USDA spokesman Aaron Lavallee said Thursday the agency received the proposal and will consider it.
The department recently launched a pilot program to encourage food stamp recipients to make more healthful choices in their food shopping. Under the program, involving 7,500 randomly selected households in Massachusetts, participants get 30 cents added to their benefit balances for every dollar they spend on fruits and vegetables - which reduces the cost of fresh produce by almost one-third.