ATLANTA — Early voting turnout in Georgia’s primary elections surged past previous milestones, signaling an energized electorate in a newly minted political battleground that remains ground zero in the national fight over voting rights, and setting off a fresh debate over a major voting law that had largely been untested before this year.Republicans quickly pointed to the early totals — more than 857,000 ballots were cast in an early voting period that ended Friday, roughly three times as many as in the same period in the 2018 primary elections — to argue that the law, passed last year by the G.O.P.-led legislature, was not suppressing votes.Democrats and voting rights groups said that the numbers were evidence that their redoubled efforts to overcome the law’s effects by guiding voters through new rules and restrictions were paying off so far, and that any focus on total turnout ignored whether voting had been made harder or had placed new burdens on marginalized groups.It is too soon to draw any sweeping conclusions, because the true impact of the voting law cannot be drawn from topline early voting data alone. The picture will grow slightly clearer on Tuesday, when Election Day turnout can be observed; clearer still in the days afterward, when final absentee ballot rejection rates and precinct-level data will emerge; and will fully come into focus after the November general election, when turnout will be far higher and put more strain on the system.The early aggregate statewide turnout figures could obscure the effects of the new law on specific groups, like Black voters, that advocates contend were targeted by it.Ultimately, election experts cautioned, it remains unclear if the law made voting harder, if Democrats have been energized by the legislation or if some combination of the two is unfolding.“Just because turnout is up doesn’t mean that voters face no hurdles,” said Richard L. Hasen, a law professor at the University of California, Irvine. “It could well mean that voters overcame those hurdles, and that means that time and money were put into efforts to assure that voters could overcome those hurdles. And that seems unjustified if those hurdles serve no important anti-fraud or other purpose.”The top election official in the state, Brad Raffensperger, a Republican running for re-election, underlined his confidence in the state’s elections under the new law, adding that he was sure county elections administrators would be adequately prepared for what will most likely be a steep increase in voter participation on Election Day.“It’s been tested and it’s coming through with straight A’s,” he said in a recent interview. “We’re having record turnout. We have record registrations, and lines have been short. Everything’s really been running very smooth.”Brad Raffensperger, a Republican and Georgia’s secretary of state, is running for re-election.Audra Melton for The New York TimesGeorgia was one of the first states to pass a new voting law after the 2020 election, when former President Donald J. Trump targeted the state with a flurry of falsehoods about its results.Republicans in the legislature passed the voting law to address what they argued were widespread problems with election oversight and expanded ballot access that could create openings for voter fraud. (Multiple recounts and audits after the election found no evidence of meaningful fraud or other wrongdoing.) Other states soon followed: At least 19 passed 34 laws last year that included new restrictions on voting or changed the way elections are administered.Democrats, civil rights groups, businesses and voting rights organizations denounced the Georgia law. President Biden called it “Jim Crow 2.0,” and Major League Baseball moved its All-Star game out of Atlanta in protest. But some of the public outcry focused on provisions that ended up being removed from the final version, such as banning voting on Sundays (the law allows counties the option of providing Sunday voting, and added a second mandatory Saturday of early voting).In this week’s primary, there are no major statewide battles for a Democratic nomination, with Stacey Abrams running largely uncontested for governor and Senator Raphael Warnock running as an incumbent for re-election. In the three weeks of early voting, 483,149 Republicans voted early, compared with 368,949 Democrats.The law instituted new regulations for mail voting, such as additional identification requirements and limits on how drop boxes could be deployed. During the 2020 election, counties across the state relied heavily on drop boxes, which were permitted by a ruling from the state’s election board, to help voters returning absentee ballots.But the new law sought to rein in their use, capping the number of drop boxes at one per 100,000 registered voters in a county — which could cut the amount of drop boxes in urban areas by as much as two-thirds — and limiting their availability to office hours. The law did, however, codify drop boxes as an option for voters into state election law.Overall turnout for absentee voting has been difficult to parse so far.During the 2020 election, when voters turned en masse to mail ballots because of the pandemic, more than 1.1 million Georgians voted by mail in the primary, and in 2018, fewer than 30,000 voted absentee. This year, more than 61,000 voted absentee in the primary, an increase over 2018 but less than 10 percent of the 2020 totals.Voters in primaries also tend to be more motivated and engaged than general-election voters, and they are more likely to be aware of new rules and willing to work through them to cast ballots.“The people who are highly engaged are the people who are voting in primaries, and those highly engaged people are often most equipped to get around any sort of change to voting,” said Michael McDonald, a voter turnout expert at the University of Florida.Gov. Brian Kemp, campaigning in the final days of his Republican primary race for governor, condemned Democrats for their criticism of the law, suggesting that their claims that it was “suppressive” were hyperbolic and politically motivated.Understand the Battle Over U.S. Voting RightsCard 1 of 6Why are voting rights an issue now? More