Unofficial returns show Kemp with an advantage, and he's already resigned as secretary of state to start a transition with the blessing of the outgoing GOP governor, Nathan Deal. President Donald Trump weighed in with a tweet that said Kemp "ran a great race in Georgia - he won. It is time to move on!"
Yet Abrams, who hopes to become the nation's first black woman governor, sent out volunteers and campaign staff in search of votes that she hopes could still tilt the margin toward her.
In a frantic effort to make sure every possible vote is counted, dozens of volunteers converged on a warehouse-turned-phone bank near downtown. The goal: reach voters who used a provisional ballot to make sure they take steps to ensure their vote - for Abrams or Kemp - is counted by Friday evening, the deadline.
Helen Brosnan of the National Domestic Workers Alliance shouted, "How many calls do you think we can make? Can we make hundreds of calls? Let's do this!"
A majority-black county with more than 750,000 residents in metro Atlanta, DeKalb, said it would remain open past normal hours Friday to accommodate provisional voters who needed to provide identification so their votes could be counted.
But two groups supporting Abrams' call to count all votes, ProGeorgia and Care in Action, said at least 12 other counties had certified election results before Friday, a move that could leave provisional ballots uncounted. The secretary of state's office did not immediately respond to an email seeking comment.
Abrams' lawyers are exploring options to ensure all votes are counted. Her campaign leaders say they believe she needs to pick up about 25,000 votes to force a runoff.
At least 2,000 people across the nation are involved in that effort, said state Sen. Nikema Williams, the Georgia director for Care In Action, which advocates for more than 2 million domestic workers and care workers nationwide.
"We're in the cradle of the civil rights movement, the home of Congressman John Lewis who literally bled on the bridge at Selma to make sure that everybody had the right to vote," she said.
Marisa Franco, 27, saw a friend's Facebook post about the effort, then showed up at the warehouse to volunteer Friday morning.
"I think that it's really central to democracy that everybody who is eligible to vote can vote and has the least amount of barriers possible, so I'm just here to make sure that every vote counts," she said.
On Friday night, a judge ordered Dougherty County to accept absentee ballots postmarked by Election Day and received by Friday.
The Abrams campaign filed a complaint in federal court asking for an injunction to direct the board of elections to count any absentee ballots received between 7 p.m. on Election Day and close of business Friday, which is consistent with the way that counting overseas military and overseas citizens' ballots is handled.
Races for governor and U.S. Senate also are tight in Florida, which Trump referred to in a tweet that said: "You mean they are just now finding votes in Florida and Georgia - but the Election was on Tuesday? Let's blame the Russians and demand an immediate apology from President Putin!"
Trump's message refers to allegations that Russian interference helped him win in 2016, but it wasn't clear exactly what the president meant about votes being found.
Returns show Kemp with 50.3 percent of almost 4 million votes, a roughly 63,000-vote lead over Abrams. That's a narrow sum, considering the near-presidential election year turnout, though sufficient for the majority required for outright victory.
The Associated Press has not declared a winner in the race for Georgia governor. The AP will reassess the race Tuesday, the deadline for counties to certify election results to the state.
With legal wrangles opening and Abrams showing no signs of conceding, the dispute is prolonging a bitter contest with historical significance and national political repercussions.
Abrams' campaign manager, Lauren Groh-Wargo, said Kemp was to blame for problems because he was the secretary of state, Georgia's top election official, and tried to tamp down minority votes.
"These suppressive tactics are reminiscent of the Old South, tactics that have been resurrected by Brian Kemp, who forced the state to allow him to oversee his own election, and had him be the decider on who was the winner," she said at a news conference.
Kemp contends he did his job properly and has argued that Abrams wants to help noncitizens vote illegally. Kemp, who has echoed Trump's immigration rhetoric, cited a speech in which Abrams said "undocumented" people were part of her coalition.
Abrams would become the first black woman elected governor of any U.S. state. Kemp seeks to maintain Republican dominance in a growing, diversifying Deep South state positioned to become a presidential battleground.
The key question is how many uncounted ballots actually remain.
Kemp said Thursday that it's fewer than 21,000 - almost certainly not enough to force a runoff. Abrams' campaign argues the total could be higher, and the secretary of state's office has shared scant details as officials in Georgia's 159 counties keep counting.
Abrams' campaign has reserved television advertising time and started sending vote-by-mail information to supporters in case she forces a Dec. 4 runoff with Kemp.
AP writer Errin Haines Whack contributed to this report.
Follow Barrow on Twitter at https://twitter.com/BillBarrowAP.
For AP's complete coverage of the U.S. midterm elections: http://apne.ws/APPolitics
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