BELFAST, Maine — Deeming their first plan too weak, the Belfast City Council has mothballed a proposed fee on single-use plastic bags and instead wants to consider an outright ban.

“We were not brave enough in our initial approach,” Councilor Eric Sanders said during a meeting Tuesday night.

Belfast has been floating the idea since September, when a group of residents proposed a ban with the goal of reducing the number of plastic bags making their way into Penobscot Bay.

The city crafted an ordinance that would have charged shoppers a 5-cent fee for each single-use bag they took out of a store, but the rule only applied to stores over 10,000 square feet with a certain percentage of food sales. Only a couple stores in the city — Ocean State Job Lot and Hannaford — would have been affected.

The proposal drew criticism from some activists for being too weak and not reaching far enough to curb the use of single-use plastic bags.

During a meeting last month, councilors largely agreed that a small fee that only applied to a couple stores wouldn’t go far enough, so they tabled the draft and decided to come up with a newer, harder-hitting idea. The council expects to hash out a new proposal during a workshop next week.

Most councilors on Tuesday night signaled that they want to come up with an ordinance that prohibits stores across the city from giving single-use plastic bags to customers. Customers could either bring their own, or the stores could provide provide non-petroleum-based bags.

The council will have to hash out some questions, such as how to define a reusable bag, whether stores should be allowed to continue giving out single-use paper bags, and what penalties stores should face for violating the ordinance.

Other midcoast towns are starting to consider bag bans or fees of their own.

Windplanners, a group of sustainability-minded students from Camden Hills Regional High School that recently led an effort to switch the school from plastic utensils to silverware to cut down on plastic waste, has set its sights on bags next.

“We have been planning to begin going door to door to businesses in Camden and Rockport to provide them with information about the single use plastic bag and its impact on the environment and specifically the area around us,” said Marco D’Amato, a Windplanners member and junior at the high school. That effort could lead to a request for a ban or a fee in Camden and Rockport in the future.

The Rockland City Council is in the early stages of weighing a plastic bag ban or fee following a resident’s request.

During the past two years, at least seven municipalities in southern Maine have either banned or taxed single-use plastic bags, including Portland, South Portland, Falmouth, York, Kennebunk and Freeport.

Saco’s city council voted just this week to ban single-use plastic bags, according to the Journal Tribune. Their ordinance requires that businesses make non-petroleum-based bags available.

Saco, like many towns, will still allow distribution of smaller plastic bags like those used for wrapping produce and meats, delivering newspapers or picking up after dogs.

Bangor’s council tossed around the idea of a plastic bag fee last summer, but the proposal failed to gain traction. It could be revived in the future.

Follow Nick McCrea on Twitter at @nmccrea213.