ATLANTA (AP) — Republican Brian Kemp’s campaign declared victory Wednesday in the Georgia governor’s race, though Democrat Stacey Abrams insists that enough ballots remain to leave open the possibility of a runoff in a race that Kemp oversees as secretary of state.

The Associated Press has not called the contest.

Ryan Mahoney, a top Kemp campaign adviser, told reporters in a conference call that the numbers show Abrams can’t win and a runoff won’t happen — but stopped short of declaring victory until pressed by an Associated Press reporter. Only then did Mahoney say Kemp is certain of victory and preparing to take office in January.

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“We are declaring victory,” Mahoney said. Another campaign official, Austin Chambers, added: “The message here is pretty simple: This election is over, and the results are clear.”

Kemp was not on the call but is expected to speak publicly on Thursday, the same day that a federal judge in Atlanta holds the first hearing on an Election Day lawsuit that seeks to have Kemp barred from having any further role in managing the election.

The Abrams campaign responded late Wednesday that Kemp’s state office had not shared with the public or with the Abrams’ campaign the detailed data behind his claims, instead asking Georgians to take him at his word.

“The sitting secretary of state has declared himself” the winner, said Abrams’ campaign manager Lauren Groh-Wargo. “We don’t accept or reject what he said. He needs to show proof.”

The stand-off leaves open the possibility of litigation as Abrams’ campaign has spent the day pushing for the continued counting of absentee, mail-in and provisional ballots and renewing its concerns that Kemp remains the chief elections officer supervising his own election, a race already marked by disputes over the voting process.

With reported votes exceeding 3.9 million — almost 95 percent of Georgia’s 2016 presidential turnout — Kemp has just more than 50 percent.

Before the Kemp campaign declared victory Wednesday, Groh-Wargo estimated that about 15,000 votes separate Kemp from a runoff. She says at least that many outstanding absentee and mail-in ballots remained to be counted.

Kemp’s spokeswoman in the secretary of state’s office, Candice Broce, said that by Wednesday afternoon the number of uncounted absentee and mail-in ballots was less than 2,000 — with her boss still above the 50 percent threshold.

Broce said about 22,000 provisional ballots have yet to be processed, according to a canvass of county officials across the state. Mahoney asserted that those numbers make it impossible for Abrams to pick up enough votes to deny Kemp an outright victory.

In 2016, with a slightly larger electorate, there were 16,739 provisional ballots. Of those, 7,592 were counted. State and campaign officials said they expected a much higher proportion to be counted this year.

Kemp’s office has not released a county-by-county breakdown of provisional ballots, but Abrams’ campaign said they believe they are concentrated in metro Atlanta counties where Abrams won a large share of the vote. Broce said Kemp’s office is working on releasing more detailed information.

If a runoff is necessary, the second round would take place Dec. 4, extending one of the marquee races of the November midterms as Abrams tries to become the first black woman elected governor in American history while Kemp looks to maintain the GOP’s domination in a state evolving into a genuine two-party battleground.

Either way, Georgians are sure to see a new round of bitter recriminations over ballot access and voting rights that could leave some voters questioning the outcome of a contest both nominees have described as a “battle for the soul of our state.”

“This is why we had a steady drumbeat for him to resign,” Groh-Wargo said Wednesday, noting Abrams’ and others’ warnings about the potential for chaos in a tight election. “Here we are,” she said.

Kemp, 55, told his supporters early Wednesday that “there are votes left to count, but we have a very strong lead. ... The math is on our side to win this election.”

His cushion for an outright majority later shrank after more ballots had been counted. So far, turnout exceeds the 2014 governor’s race by about 1.3 million votes.

Kemp’s office, meanwhile, deflected the criticisms.

Broce noted local elections authorities manage the voting process and ballot tabulation. “Counties have not completed certification and we are still waiting for counties to provide their tabulations leading up to that certification,” she said.

A nonprofit group, Protect Democracy, filed a lawsuit Tuesday seeking to keep Kemp from being involved in counting votes, certifying results or any runoff or recount. Broce called it a “twelfth-hour stunt.”

State law gives counties until next Tuesday to complete vote counts and certify results to state elections officials. The statewide certification must follow by Nov. 20.

The indefinite extension in Georgia focuses a white-hot spotlight on a race that already has drawn massive investments of time, money and star power — from President Donald Trump and former President Barack Obama to media icon Oprah Winfrey.

The tight returns and potential runoff come after weeks of wrangling over Georgia’s election system and Kemp’s performance as its chief executive. Kemp has steadfastly defended his job performance and refused calls to step aside.

Abrams, 44, has called Kemp “an architect of suppression,” and voting rights activists expressed concerns throughout Tuesday amid reports of technical malfunctions and long lines at polling stations across the state.

The elections chief wasn’t immune to the difficulties: When Kemp went to cast his own ballot, he had an issue with his voter card, but it was fixed quickly.

In the closing days, Kemp basked in Trump’s glow, pulling out of a debate to attend a Sunday rally that drew thousands of boisterous Republicans to central Georgia to see Trump deplane from Air Force One.

Abrams answered with Obama and Winfrey.

Even if Abrams ultimately falls short, she has outperformed her fellow Democratic nominees from recent election cycles.

That validates her strategy of reaching out to nonwhite and younger voters who don’t usually cast midterm ballots instead of Democrats’ previous focus on trying to convert older white voters who’d long drifted toward Republicans.

Her success came at a cost, however, as unofficial returns showed Kemp expanding the GOP’s advantage across rural and small-town Georgia.

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Follow Barrow and Nadler on Twitter at https://twitter.com/BillBarrowAP and https://twitter.com/benjaminrnadler .

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For AP’s complete coverage of the U.S. midterm elections: http://apne.ws/APPolitics