Mr. Cuomo’s opposition to the city measure was similarly centered on the fee structure; he said at the time that the bill was “deeply flawed” because it allowed merchants to keep the 5-cent fee as profit, a giveaway that he said would total $100 million a year.

Brad Lander, Democrat of Brooklyn, the councilman who led the city’s effort to impose a 5-cent fee, called Mr. Cuomo’s proposal a transparent political maneuver.

“I wish I believed the governor was serious about reducing the billions of single-use plastic bags New Yorkers are sending to landfills every year, but this looks like election-year, Earth Day politics,” Mr. Lander said.

Susan Brockmann, one of hundreds of demonstrators who filled the State Capitol on Monday to rally for stronger environmental protections, said that New York should emulate California.

“It’s time,” said Ms. Brockmann, 55, a midwife from Long Island who was dressed in a suit made of 500 plastic bags. “We should follow the lead of other progressive communities.”

Monday’s proposal came as a result of a report in January by a task force that Mr. Cuomo convened last year after blocking the city bill. A ban was one of eight options entertained by that report, though it also outlined a number of drawbacks, including the fact that paper bags, an alternative to plastic, cost retailers “three to five times as much as single-use plastic bags.”

Under Mr. Cuomo’s proposal, a variety of bags would be exempted from the ban, including those that contains raw meat, fish or poultry; bags sold in bulk; those used in bulk packages of fruit and dried goods; those used for deli products; newspaper bags; trash, food storage and garment bags; and takeout food bags. The state’s Department of Environmental Conservation would also be allowed to exempt certain bags through regulations.