Republican Brian Kemp's campaign declared victory in the race for Georgia governor on Wednesday, even as election officials continued counting thousands of absentee and provisional ballots, narrowing his lead and prompting Democrat Stacey Abrams to insist she could have the votes to force a runoff election.

As the vote-counting continued, voting rights advocates accused Mr Kemp – who as secretary of state is Georgia's top election officer – and local officials of disenfranchising thousands of voters on Election Day. Hundreds of complaints flooded in about hours-long lines brought on by broken equipment, a shortage of voting machines and insufficient quantities of printed provisional ballots.

On Wednesday evening, Mr Kemp was ahead with 50.3 per cent of the vote to Ms Abrams's 48.7 per cent. Ms Abrams and the libertarian candidate would need to gain at least 25,000 votes more than Mr Kemp to bring his share of the vote below 50 per cent and trigger a runoff.

"We believe our chance for a stronger Georgia is just within reach," Ms Abrams, who if elected would be the nation's first black female governor, told supporters early on Wednesday. "We cannot seize it, however, until all voices are heard. And we are going to make sure that every vote is counted – because in a civilised nation, the machinery of democracy should work everywhere for everyone."

The secretary of state's office reported late on Wednesday that fewer than 3,000 regular ballots remained to be counted state-wide and a total of 22,000 provisional ballots had been cast – numbers that would likely close off any path to victory for Ms Abrams. The office did not certify a winner and said votes could be counted into next week.

Yet Cody Hall, a spokesperson for Mr Kemp's campaign, said: "Abrams does not have a mathematical formula to victory, based on our calculations. We have a clear path to victory. We're declaring victory and we are moving forward with the transition process starting tomorrow."

In a statement on Wednesday, the Abrams campaign claimed that nearly 100,000 ballots, and possibly more, remained uncounted.

Among the calls logged at a voter hotline run by a consortium of voting rights groups including the NAACP, the American Civil Liberties Union and Common Cause were complaints from hundreds of voters who said their requests for absentee ballots went unanswered. Voters – and advocates – said they were chagrined at how many of those reports came from communities with large minority populations.

"From our vantage point, this was an intentional system failure in targeting communities where African-Americans made up a high percentage of active voters," said NAACP President Derrick Johnson.

Peggy Xu, 23, was one of those voters. Ms Xu provided emails to The Washington Post showing she requested an absentee ballot from Fulton County on 6 October and said she later saw on the secretary of state's website that one had been sent to her. But she never received it, she said. She tried again, did not receive the second ballot either and was not able to vote, she said.

"I'm furious," she said. "I was genuinely excited to vote for her. But now, seeing this razor-thin margin and seeing how many voter suppression issues are going on, it is driving me a little crazy, especially knowing that this has affected so many voters."

Asked about the range of voter concerns, Candice Broce, a spokesperson for the secretary of state's office, noted the turnout shattered midterm records.

"I stand confident that we had a successful Election Day," she said.

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In addition, election monitors from civil rights groups said hundreds of voters whose registrations had been suspended under a strict new law, one championed by Mr Kemp, were improperly turned away. The law requires personal information on registration applications, even down to the hyphen, exactly match other government records. In late October, a federal judge ordered the state to alert such voters before removing them from the rolls and to allow them to vote with proper identification.

Another problem was the limited number of voting machines in some locations. More than 1,800 machines sat idle in storage in three of the state's largest and most heavily Democratic counties. In Fulton County, according to figures provided by elections director Rick Barron, the ratio of machines to registered voters was lower than it had been in 2014, despite predictions that turnout was likely to break records for a midterm election.

While some voters waited in hours-long lines in Fulton County, 700 of those machines sat in stacks in a warehouse in downtown Atlanta, Mr Barron said. The machines were side-lined because they are evidence in a lawsuit alleging the equipment had been exposed to the threat of hacking in 2016.

The federal judge in the case had ordered state and local election officials – including Mr Kemp – and the plaintiffs to weigh the demands of upcoming elections in deciding how many machines to set aside.

In an interview, Mr Barron said more machines "would have made a huge impact on operations yesterday" and acknowledged "it would have been a good idea" to push for the use of more machines before Election Day.

"The lines were long in the morning and we just didn't have any machines to throw out there," he said.

Ms Broce, too, said additional machines "would have really helped with the long lines."

She blamed the litigation for tying up those machines. One attorney for the plaintiffs, Bruce Brown, called that "rubbish" and said officials could have sequestered fewer machines, or later decided to put some back into service.

Daniel White, an attorney representing Cobb and DeKalb counties, said both counties kept more machines out of circulation on Tuesday than required by the judge "out of an abundance of caution" that they were complying with the spirit of the court agreement.

Mr White said he suspected the sequestered machines contributed to long lines at his polling place on Tuesday. At a school in Marietta, where Mr White said he usually sees eight to 12 machines, he saw just five or six.

Tuesday's ballot was long, with five constitutional amendments across the state and additional measures in select locations.

One precinct near Pittman Park in downtown Atlanta started the day with just three machines, despite a registered voter roll of more than 3,000. Similar equipment problems were reported elsewhere in Fulton County and in three other large counties of the Atlanta metro area - Cobb, DeKalb and Gwinnett.

Ms Abrams's campaign manager Lauren Groh-Wargo said the problems were Mr Kemp's responsibility. "Machines were breaking down and counties did not get guidance from the secretary of state and didn't have adequate paper ballots - let's be clear about where the blame lies," she said.

Ms Broce said local officials make those decisions, not the secretary of state.

"Counties are the custodians of the equipment and are responsible for deploying it," she said.