DOVER — The Delaware General Assembly has passed a bill to decriminalize possession of marijuana for personal use.

The Delaware Senate on Thursday voted 13 to 7 to pass the bill, one week after the House of Representatives did the same. The bill would remove penalties for having one ounce or less of marijuana, except for those under 21 years old.

The bill is “a critical first step that will protect one in five Delawareans and restore the rights and freedoms for conduct that’s legal in 18 states now,” said Zoë Patchell, executive director of the Delaware Cannabis Advocacy Network, which has pushed for legislation to legalize recreational pot usage for almost a decade now.

Possessing more than one ounce of marijuana as well as consuming weed in public would still each be a misdemeanor if the bill, HB371, becomes law.

For it to do so, it will need to overcome a likely veto from Gov. John Carney, who has voiced his opposition to recreational marijuana use. The governor will review the bill, said Emily David Hershman, his communications director, but “the Governor’s position hasn’t changed.”

Noting the broad support for legalization in the state, Sen. Trey Paradee, D-Dover, touted the bill as both a social and economic good. Legalization would stop possession charges from “ruining peoples’ lives,” he said, and put an end to the disproportionate impacts of those arrests on people of color.

Taxing purchases of legal cannabis — should a companion bill setting up a regulatory framework for marijuana make it into law — would mean more money for things like schools and fighting the opioid epidemic, Mr. Paradee claimed.

“We have to ask ourselves, ‘Where is the revenue going now?’ Right? Because marijuana is very available on the streets of Delaware. So somebody’s making money. Well, I’ll tell you who: It’s drug gangs. It’s cartels,” Mr. Paradee said. “It’s New Jersey.”

The bill passed over the opposition of every Senate Republican. (Democratic Sen. Bruce Ennis, Smyrna, also gave a thumbs-down to the legislation.) Multiple lawmakers voiced concerns during the hearing about the potential consequences of legalization — ranging from fears over increasing the number of Delawareans driving under the influence to ensuring a regulatory framework would be in place before the current legislative session ends June 30.

Sen. Colin Bonini, R-Dover, said it would be a mistake to pass decriminalizing legislation without the proper regulatory framework in place. That framework is contained within a separate companion bill, HB372, which needs the approval of three-fifths of lawmakers in each chamber.

As it stands, Mr. Bonini said, “There’s no revenue in here. There’s no regulation at all here.”

Mr. Paradee promised his colleague he would personally ask the governor to veto the decriminalization bill if the legislation that would regulate marijuana fails to pass. Mr. Bonini was not persuaded; his was among seven downvotes.

“We still have a long way to go” before both bills become law, Ms. Patchell said. She, like Mr. Paradee, noted the strong public support for legalizing marijuana.

“We’re really hoping that the Delaware legislature listens to the will of the supermajority of Delawareans that support this measure and prioritize it as soon as possible,” she said.