The Associated Press had Kemp with 51 per cent of the vote to Abrams’ 48 per cent as of 1:45 a.m. ET, with 96 per cent of polls reporting.
“Votes remain to be counted. There are voices that are waiting to be heard,” said Abrams, who served as minority leader of the Georgia House of Representatives from 2011 to 2017 and is bidding to become the first black female governor in U.S. history.
WATCH: Abrams makes final push on Election Day, says ‘it’s not just about me’
“In a civilized country, the machinery of democracy should work for everyone, everywhere. Not just for certain places and not just on a certain day,” she added.
“You’re going to have a chance to have a do-over.”
Voting stations in Georgia were plagued with long lines and malfunctioning machines on Tuesday.
At a polling place in Snellville, Georgia, more than 100 people took turns sitting in children’s chairs and on the floor as they waited in line for hours.
Voter Ontaria Woods said about two dozen people who had come to vote left because of the lines.
WATCH: Fears of voter suppression after problem at Georgia polling station
The contentious gubernatorial race between Abrams and Kemp, who is Georgia’s secretary of state, has been marred by accusations of voter suppression.
Last month, voting rights advocacy groups sued Kemp, whose role makes him Georgia’s top election official, accusing the Republican of placing voter registrations on hold to boost his campaign.
WATCH: Brian Kemp votes in Georgia gubernatorial race
Former U.S. President and Georgia Governor Jimmy Carter asked Kemp to resign his position as Georgia’s secretary of state, saying his role in state government imperiled popular confidence in the election.
Also in October, the group Black Voters Matter, which encourages African-Americans to vote, said that some 40 black residents of a senior living centre were told to get off a bus taking them to a polling place to cast their early ballots.
Kemp also attracted controversy this past weekend after his office said it was investigating the Georgia Democratic Party in connection with an alleged attempt to hack the state’s online voter database.
WATCH: Abrams slams Kemp over investigation into hacking allegations, says he’s created a ‘hoax’
His office offered no evidence to support its claim, but the allegation nevertheless became a flashpoint in the race.
Abrams slammed the allegation as a “hoax,” while President Donald Trump, who has endorsed Kemp, said he didn’t know about the issue.
— With files from the Associated Press and Reuters