Republican Brian Kemp's campaign said on Wednesday he had won Georgia's high-profile governor's race, but Democratic candidate Stacey Abrams vowed not to concede until all ballots were counted.

"Simply put, it is mathematically impossible for Stacey Abrams to win or force a run-off election," Kemp spokesman Cody Hall said in a statement Wednesday evening. "Brian Kemp will now begin his transition as governor-elect of Georgia."

Abrams, 44, is trying to become the first black woman elected governor of a U.S. state. Unofficial results from Tuesday's election showed Kemp leading by more than 60,000 votes and just over the 50 percent threshold he needs to avoid a runoff under Georgia state law.