ATLANTA — Brian Kemp, the Republican who has claimed victory in the Georgia governor’s race, said on Thursday that he was resigning as secretary of state, removing himself from the process of determining whether he had in fact been elected.
With some ballots still to be counted, his Democratic opponent, Stacey Abrams, is just shy of enough votes to force a runoff. Ms. Abrams has not conceded, and The Associated Press and other major news organizations say the race is still too close to call.
Mr. Kemp attracted mounting criticism during the campaign for his management of an election in which he was also a candidate, but he had dismissed repeated calls from Democrats for him to resign in the weeks before Election Day.
Mr. Kemp made no mention of the elections process on Thursday in his resignation letter to the outgoing Republican governor, Nathan Deal, saying he was resigning because he wished “to focus on the transition to my gubernatorial administration.”
Appearing with Mr. Deal at a morning news conference at the State Capitol in Atlanta, Mr. Kemp said, “I think in light of where we are now, this will give public confidence to the certification process, even though, quite honestly, it’s being done at the county level.”
Robyn A. Crittenden, the commissioner of the Georgia Department of Human Services, was named acting secretary of state, and will oversee the certification of Georgia’s election results. Ms. Crittenden assumes the office at a volatile moment in Georgia, with Ms. Abrams’s campaign still raising pointed questions about the integrity of the election.
Ms. Crittenden will also supervise runoffs in at least two other statewide races, one of them for secretary of state, as well as one for governor if Ms. Abrams’s campaign succeeds in forcing one.
While prominent Republicans sent congratulations to Mr. Kemp on Thursday, Democrats did little to hide their disgust with his course of action.
“Press releases do not declare victory,” said Lauren Groh-Wargo, Ms. Abrams’s campaign manager.
As Mr. Kemp’s resignation took effect at 11:59 a.m. Thursday, his office said he had won 50.3 percent of the vote and held a lead of about 63,000 votes over Ms. Abrams. To win the governorship, Mr. Kemp must have an outright majority.
But Ms. Abrams’s campaign believes there is still a potential path to a runoff in the remaining untabulated absentee and provisional ballots.
“All the votes haven’t been counted,” John Chandler, a lawyer for the Abrams campaign, said at a midday news conference in Atlanta. “How can anyone claim a victory when there are enough votes that have not been counted that could cause a runoff here? We believe that everybody is entitled to have their vote counted.”
The Abrams campaign said it intended to file a lawsuit on Thursday concerning a southwest Georgia county where mailing of absentee ballots was delayed by an injunction and, later, by Hurricane Michael. The suit seeks an extension of the deadline for ballots there to arrive and be counted.
The campaign did not immediately announce any other litigation, saying it was considering its options.
Mr. Kemp’s office said on Wednesday that there were fewer than 25,000 remaining untabulated ballots statewide, most of them provisional. That would almost certainly be too few to force a runoff, even if they were all validated and were cast overwhelmingly for Ms. Abrams.
Ms. Groh-Wargo brushed those figures aside on Thursday. “We do not believe any of those numbers are credible,” she said.
The Abrams campaign demanded that state officials release much more data, including county-by-county breakdowns, to support their conclusions, and said that valid ballots were still turning up. The campaign is also urging voters who cast provisional ballots because of problems with their identification to visit county election offices quickly and clear up the matter so their votes can be counted.
Mr. Kemp’s resignation as secretary of state appeared to render moot a federal lawsuit filed on Tuesday by the nonprofit group Protect Democracy demanding Mr. Kemp’s recusal. A hearing in that case was scheduled for Thursday.
As Mr. Kemp and Mr. Deal spoke at the Capitol, protesters stood outside the governor’s office suite with signs demanding that every vote be counted properly. A detachment of state troopers stood guard.
Mr. Kemp’s dual roles as both player and referee in the governor’s race has infuriated Democrats ever since he won the Republican nomination. They frequently accused him of using his office to further a campaign of voter suppression, through purges of voter rolls and other disputed actions.
Jimmy Carter, who was governor of Georgia before being elected to the White House, warned Mr. Kemp in a letter that his refusal to step down before the election ran “counter to the most fundamental principle of democratic elections — that the electoral process be managed by an independent and impartial election authority.”
Over the weekend before Election Day, Mr. Kemp took a step that drew the greatest criticism of all. In a vaguely worded announcement that offered no evidence, Mr. Kemp’s office said it had opened an investigation into the Democratic Party of Georgia after “a failed attempt to hack the state’s voter registration system.”
Democrats denied any wrongdoing and condemned the investigation — and especially the public announcement of it two days before the election — as a last-minute political stunt. But Mr. Kemp once again rejected calls to step down at that time.
On Thursday morning, standing in the stately ceremonial office long used by the state’s governors, he said he would now spend his time preparing to move in.