A six-month battle over a North Carolina Supreme Court seat ended on Wednesday when the Republican challenger, who had embarked on an extraordinary effort to throw out thousands of votes, conceded the race.

The challenger, Judge Jefferson Griffin, said in a statement that he would not appeal a federal court ruling issued on Monday that ordered the state elections board to certify the victory of the Democratic incumbent, Justice Allison Riggs.

“While I do not fully agree with the District Court’s analysis, I respect the court’s holding — just as I have respected every judicial tribunal that has heard this case,” Mr. Griffin said. “I will not appeal the court’s decision.”

Two recounts affirmed that Justice Riggs won the race by a margin of 734 votes, out of the more than 5.5 million ballots that were cast. The results of the race are the last in the nation to be certified from the 2024 election.

“After millions of dollars spent, more than 68,000 voters at risk of losing their votes, thousands of volunteers mobilized, hundreds of legal documents filed, and immeasurable damage done to our democracy, I’m glad the will of the voters was finally heard, six months and two days after Election Day,” Justice Riggs said in a statement.

Judge Griffin, who currently sits on the North Carolina Court of Appeals, said on Wednesday that “as a judge, I believe everybody, myself included, has a right to their day in court.”

“This effort,” he added, “has always been about upholding the rule of law and making sure that every legal vote in an election is counted.”

The case tested the boundaries of post-election litigation, and drew criticism from democracy watchdog groups, liberals and even some conservatives across the state, who worried about setting a dangerous precedent.

Voting rights experts have said that regardless of the outcome, the unusual series of challenges from Judge Griffin, and the courts’ openness to entertaining them, may have paved the way for similar challenges in future close elections, as President Trump and his supporters try to erode confidence in the integrity of American elections.

Judge Griffin began his fight by arguing that more than 65,000 ballots that were cast in the election should not be counted because of eligibility issues. He filed a protest with the State Board of Elections after the board twice certified Judge Riggs’s victory. (The total number of ballots in question fluctuated over time as the case wound its way through the election board and the courts.)

Among the ballots he challenged were those cast by thousands of military and overseas voters, on the grounds that they had not submitted a photo ID or an ID exception form with their absentee ballots — even though the voters were exempted from those requirements before the election.

Judge Griffin also challenged the ballots of nearly 300 voters who he said were “Never Residents,” meaning they did not live in North Carolina but were registered to vote there. The “Never Residents” category typically includes North Carolinians who are working overseas and children of military parents from North Carolina who turn 18 while their family is stationed abroad. North Carolina passed a law in 2011 allowing such people to vote in the state’s elections.

In April, the State Supreme Court partially agreed with Judge Griffin, ruling that the eligibility of military and overseas voters who cast ballots in the election should be verified, and that the votes from “Never Residents” should be thrown out. Justice Riggs, who has recused herself from the case, appealed the ruling to the federal courts.

Lawyers for Judge Griffin said they were trying to enforce laws that the Board of Elections had failed to apply. The North Carolina Republican Party supported Judge Griffin’s challenge. Matt Mercer, a spokesman for the state party, said in a statement that “Judge Griffin deserves the appreciation of every North Carolinian for highlighting the appalling mismanagement” of the state elections board.

Judge Griffin’s critics noted that the ballots in question were included in certified counts for every other race in the state last November, and likened his challenge to trying to change the rules after the game has been played. The federal judge — a Trump appointee — who ordered the elections board on Monday to certify the race agreed with that argument, ruling that the “retroactive invalidation” of military and overseas ballots would be a violation of those voters’ due process rights.

This is a developing story. Check back for updates.