NEW YORK — City grocery shoppers may soon face a 10-cent fee on all plastic and paper bags, enlisting the nation’s largest city in a growing green movement.

The City Council introduced a bill Wednesday that would impose the fee in an effort to spur customers to bring their own reusable bags. Supporters of the bill say it would benefit the city’s economy as well as its environment.

“The bags get stuck in storm drains, they cause flooding and they litter our beaches,” Councilman Melissa Chen of Manhattan, a co-sponsor of the legislation, said at a news conference on the City Hall steps. “And they cost New York City a lot of money.”

City residents use 1 billion disposable plastic bags a year and it costs the city $10 million annually to ship used bags to landfills, according to the bills’ supporters.

The measure is expected to be voted on within the next few weeks. If it passes, New York will join such cities as Los Angeles, San Francisco, Seattle and Washington to try to curb the use of plastic bags.

In Portland, Maine, a task force has recommended a similar 10-cent fee on plastic and paper bags, but it drew so much opposition at a public hearing last week that a City Council committee decided to postpone its vote on the proposal.

In New York, Lilly Belanger of the environmental advocacy group the No Impact Project said Wednesday that “plastic bags are not central to our life happiness or health but make an enormous impact on our world. With this simple step, we can be a model for rest of country.”

As if to underscore their words, a plastic bag then blew above the news conference, drawing jeers from the crowd.

The 10-cent fee would not be a tax. Instead, the money raised from the bag sales would benefit the store owners who supplied the bags.

Though grocery stores supply the vast majority of the disposable bags used across the city, the fee would also apply to bags sold at other retail stores. It would not apply to restaurant deliveries or most street food carts. The fee would also not be charged to shoppers who use public-assistance programs to buy food.

Councilman Brad Lander said the fee also applied to paper bags not because the bill was intended as a method to raising revenue, but as an incentive for customers to opt for reusable bags. “Plastic is worse than paper, but it’s best if people bring their own bags,” said Lander.

Some business owners have complained that the fee could keep shoppers away. A similar measure was introduced last summer but failed to gather the necessary support and had to be re-introduced in front of the new council, which took office in January. Nineteen council members are co-sponsoring the new bill, seven short of the votes needed to pass it.

Council Speaker Melissa Mark-Viverito said Wednesday that she would need to review the bill before determining her position. Her close ally, Mayor Bill de Blasio, stopped short of endorsing the bill a day earlier but said that reducing the number of plastic bags was “a societal goal.”

“The plastic bags are a problem, and our goal has to be to reduce the use of plastic bags,” de Blasio said.