Republican Brian Kemp declared himself the winner Wednesday in the race for Georgia’s governor, saying he led Democrat Stacey Abrams by 1.6% of votes after all absentee ballots were counted.

Mr. Kemp, Georgia’s secretary of state, earned nearly two million votes, by far the most of any gubernatorial candidate in the state’s history, his spokesman, Cody Hall, said in a statement late Wednesday afternoon. Mr. Kemp will now begin his transition as governor-elect of Georgia, he said.

Campaign officials for Ms. Abrams said during an evening conference call with reporters that thousands of uncounted absentee and provisional ballots could force a runoff. Regarding Mr. Kemp’s declaration that he won the race, Abrams campaign manager Lauren Groh-Wargo said, “We do not accept that.”

Earlier Wednesday, Ms. Groh-Wargo said the campaign’s lawyers were checking with county election boards and considering litigation if necessary.

“All options are on the table,” Ms. Groh-Wargo said, adding that any resolution of the election could take weeks or longer.