Exactly how many Georgia votes remain to be counted is a topic of hot dispute. The Kemp campaign says that there are fewer than 25,000, not enough to change the outcome, but the Abrams side insists that the figures are almost certainly incomplete and that no one could yet know the precise figure.

The Abrams team has been blanketing the state’s airwaves with ads exhorting voters who cast provisional ballots to do what is required to make sure they are counted. The state Democratic Party filed a lawsuit on Thursday hoping to extend a deadline for absentee ballots in a county affected by Hurricane Michael. Lawyers elsewhere are scrutinizing the methods some counties used to reject absentee ballots.

As prominent Republicans sent congratulations to Mr. Kemp on Thursday, Democrats did little to hide their disgust at his claim of victory, which they say is premature. And in neighborhoods across Atlanta, few residents seemed to have removed the campaign signs from their front lawns.

Ms. Abrams hopes to become the first black woman elected governor of any American state, and Mr. Kemp, who is white, has been pilloried by liberals for what they say have been voter suppression tactics on his watch that disproportionately affected minority voters.

Mr. Kemp ignored calls throughout the campaign to step aside from a post that made him the supervisor of an election in which he was a candidate. But on Thursday, facing a federal lawsuit seeking to force him out, he announced his resignation.

It was hardly enough to placate the Abrams camp, which continued with a program that it said amounted to “protecting our democracy.” Mr. Kemp’s visit to the governor’s office on Thursday particularly rankled.

“He gets up at a press conference and thinks we’re all just supposed to believe that we’re moving on and this is a resolution,” said Lauren Groh-Wargo, Ms. Abrams’s campaign manager, at a news conference.