A reduced workforce contributed to officials consolidating polling places, which disproportionately affected neighbourhoods with high concentrations of people of colour. Long lines were also reported in whiter suburban areas.
Some voters said they requested mail-in ballots that never arrived, forcing them to go to polling places and adding to the lines.
Turnout may be higher than expected as voters said they were determined to exercise their constitutional right after the police killing of George Floyd in Minneapolis and the ensuing demonstrations that swept cities including Atlanta.
Former Vice-President Joe Biden easily won the state's Democratic presidential primary. He was facing no real opposition but hoped to post a strong showing among Georgia's diverse electorate to show his strength heading into the general election.
But the developments were troubling heading into the presidential campaign, which will attract even more voters. Biden and US President Donald Trump are expected to fiercely compete in this rapidly changing state.
That leaves officials, who have already been criticised for attempting to suppress the vote, with less than five months to turn things around.
Republican leaders blamed the meltdowns on officials in Fulton and DeKalb counties, which are Democratic strongholds with significant black populations.
"When these things arise, and it's really specifically in one or two counties ... it leads us back to the failure of the management of the county election directors in those counties," Republican Secretary of State Brad Raffensperger said. "It has nothing to do with what we're doing in the rest of Georgia."
Republican House Speaker David Ralston directed leaders of the House Governmental Affairs Committee to investigate the "unacceptable deficiencies" across the state, particularly in Fulton County.
Fulton County election director Richard Barron said the pandemic and large increase in mail voting "created unique staffing and logistical challenges." He said his team had "identified several areas for improvement" in November.
Democrats insisted the issues were more widespread. About 400km from Atlanta, Savannah Mayor Van Johnson said he was "inundated" with phone calls from voters reporting "extensive delays."
The Trump campaign seized on the problems to amplify the President's broader opposition to expanded mail voting.
"The chaos in Georgia is a direct result of the reduction in the number of in-person polling places and over reliance on mail-in voting," said Trump campaign senior counsel Justin Clark. "We have a duty to protect the constitutional rights of all of our citizens to vote in person and to have their votes counted."
The Biden campaign called the voting problems in Georgia "completely unacceptable" and a threat to free and fair elections.
"We only have a few months left until voters around the nation head to the polls again, and efforts should begin immediately to ensure that every Georgian - and every American - is able to safely exercise their right to vote," said Rachana Desai Martin, the campaign's national director for voter protection and senior counsel.
Americans also voted in primaries in West Virginia, South Carolina and Nevada, where hours-long lines were reported as well. But the tumult in Georgia garnered much of the attention, reinforcing concerns about managing elections amid the coronavirus.
Outside a recreation centre being used as a polling site in Atlanta, some voters said they had been waiting for nearly four hours in a line that wrapped around the block. At another site off Atlanta's Piedmont Park, several people walked up, looked at the line wrapped around the parking lot and then left, shaking their heads in frustration.
Atlanta Mayor Keisha Lance Bottoms said voters in line at one of Atlanta's largest precincts reported all the machines were down. She encouraged voters not to give up.
"If you are in line, PLEASE do not allow your vote to be suppressed," the Democratic mayor tweeted.
Democratic National Committee Chairman Tom Perez said he wasn't surprised that Georgia had voting problems given that the state's elections chief is a Republican. He noted that GOP Governor Brian Kemp faced allegations of suppressing votes when he oversaw the 2018 elections as secretary of state.
"Republicans want to ensure that it is as hard as possible for people to vote," Perez said.
Georgia hasn't voted for a Democratic presidential candidate since 1992, but the state is being closely watched by Trump and Biden. The former Vice-President, in particular, hopes to emerge as the prime beneficiary of energy from the African American community and its white allies, who have held massive protests for more than a week.
- AP