SEATTLE — The City Council here voted unanimously on Monday to ban plastic grocery bags and charge a 5-cent fee on paper bags — and this time city leaders hope the ban actually takes effect.

Three years ago, Seattle city officials became the first in the nation to approve a fee on paper and plastic bags, instituting a charge of 20 cents for each bag provided by many retail stores. The idea was to create a financial incentive to reduce pollution: the fee was supposed to prompt people to bring reusable bags with them to shop.

But before the 2008 fee took effect, the plastic-bag industry led a petition drive that forced the issue onto a citywide ballot. In August 2009, in the midst of the recession and after the industry spent $1.4 million on the campaign, Seattle voters rejected the fee.

“Twenty cents felt kind of punitive, especially for low-income folks,” said Mike O’Brien, a council member whose committee introduced the current bill.