ATLANTA — After Georgia lawmakers failed to act on their self-imposed deadline to overhaul the state’s election machinery, a panel of appointees to the board that regulates elections narrowly voted Wednesday to consider a rule that would require hand-marked paper ballots.

Two years ago, the Legislature passed a law that makes the current voting system illegal starting July 1. The law bans the use of computer-generated codes to tabulate votes. The current system relies on a tailored Quick Response, or QR, code that kiosks print after each voter completes their ballot.

In the two years since they banned QR codes, lawmakers did not authorize an alternative system. Instead, they blamed Secretary of State Brad Raffensperger for not finding an affordable option. The Republican pointed back at them, saying it was their job to designate and pay for a new system.

The State Election Board met in a hastily convened online session Wednesday. After debating whether they had the authority to step in, they voted 3-2 to hold a working meeting next week with the Coalition for Good Governance.

That is the group that petitioned for the new rule. The Coalition wants to use the state’s emergency backup balloting system for the general election in November, despite concerns from local election officials that they lack time to implement it at scale.

That system, intended for power outages and computer failures, uses preprinted ballots that voters mark by hand. Scanners then tally their votes using the marks.

The Coalition’s executive director, Marilyn Marks, said at the hearing that such an overhaul would not be “a piece of cake” but would be possible.

She urged the board to ignore the July 1 deadline on QR codes, arguing that the system already violates other federal and state laws for secret and secure balloting.

If the state fails to implement a different system soon, she argued, it will undermine confidence in election integrity and invite lawsuits, making the outcome of elections contested and uncertain.

“With all the attention and with an entire state operating a system that is not in legal compliance, Georgia’s begging for problems,” Marks said.

The election board members were divided on what to do next, with some afraid of overstepping their legal authority.

The chairman, John Fervier, who was appointed by Gov. Brian Kemp, said there was “a more than reasonable chance” that Kemp would call lawmakers back to the Capitol for a special legislative session to solve the problem.

“I think this has been a legislative issue all along. They created this problem,” Fervier said. “They haven’t resolved this problem, and they deserve a right to resolve the problem before we do.”

He voted against the proposal to collaborate with Marks’ group.

But two other Republican appointees, Salleigh Grubbs and vice chair Janice Johnston, were more concerned about the approaching deadline.

Johnston said she supported switching to paper ballots as soon as possible.

Grubbs made a motion to collaborate with Marks’ group next week. The goal would be to refine the language that the board would adopt as a rule that applied to all Georgia election directors. No Republican would second it, and Fervier was about to move on, when Sara Tindall Ghazal, the panel’s sole Democratic appointee, seconded it.

The subsequent voting was by voice, with all members off screen except Grubbs, who could be seen voting yes. Johnston confirmed to Fervier that she had also voted yes, and Fervier said he was voting no.

It was unclear whether the third supporting vote was voiced by Ghazal or by Janelle King, an appointee of the Republican-led state House.

With that vote recorded, up to two members of the board can now help Marks’ group craft a proposed rule.

They are up against a hard deadline. The board would have to hold another special meeting next week for a formal vote to initiate rulemaking to publish a new rule by July 1.

The process takes so long because the board must open any proposed rule for a 30-day public comment period before taking final action. The last scheduled opportunity to approve a new rule before July is the board’s scheduled meeting in June.

To meet that deadline while adhering to the public-review requirement, the board must transmit a petition for rulemaking to the Legislature by May 4.

“It felt like a good, productive step today,” Marks said after the hearing. She said she hoped for a “robust” public discussion on the petition.