Three days after the runoff elections in Georgia that secured full congressional control for Democrats, Senator David Perdue acknowledged his loss to his Democratic challenger, Jon Ossoff.

Mr. Perdue’s concession on Friday, coupled with Senator Kelly Loeffler’s concession to Senator-elect Raphael Warnock a day earlier, ensures that the results of the Georgia runoffs will not be subject to the prolonged, baseless challenges that President Trump raised to his own loss in the state.

“Although we won the general election, we came up just short of Georgia’s 50 percent rule, and now I want to congratulate the Democratic Party and my opponent for this runoff win,” Mr. Perdue said in a statement. In the November election, he received 49.7 percent of the vote to Mr. Ossoff’s 47.9 percent, but Georgia requires a runoff if no candidate reaches 50 percent — ironically, a system that historically benefited conservative candidates by reducing the power of Black voters.

With roughly 98 percent of votes counted, Mr. Ossoff is ahead by 45,000 votes, or about a percentage point: more than three times the number of votes that President-elect Joseph R. Biden Jr. won the state by, and double the margin that would have allowed Mr. Perdue to seek a recount.

Mr. Ossoff and Mr. Warnock will be sworn in once Georgia election officials certify the results — most likely by the time Mr. Biden is inaugurated on Jan. 20. That will create a 50-50 split between Democrats and Republicans in the Senate, with Vice President-elect Kamala Harris breaking ties, and end six years of Republican control of the chamber.

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