Democrats have cemented their control of the US Senate by winning a bitterly fought seat in Georgia, according to projections.

Raphael Warnock fended off Republican challenger Herschel Walker in a race that had been left undecided after last month’s midterm elections.

President Joe Biden’s party now holds the upper chamber of Congress by 51-49. The result caps a disappointing round of midterm election results for the Republicans. The party underperformed expectations last month by winning only a slender majority in the US House of Representatives, Congress’ lower chamber.

Mr Walker, an American football legend and political newcomer, joins a string of defeated candidates endorsed by former President Donald Trump, who is currently seeking the Republican White House nomination again in 2024.

Georgia’s contest had to be settled by a run-off vote because no candidate passed 50% of the vote in November, although Mr Warnock had led Mr Walker by 37,000 votes cast.

Mr Warnock – who became the first black senator in the Deep South state when he first won his seat in January 2021 – told his victory party at an Atlanta hotel ballroom: “It is my honour to utter the four most powerful words ever spoken in a democracy: the people have spoken!”

The 53-year-old southern Baptist preacher, whose Atlanta church was once led by civil rights leader Martin Luther King, gave a special thank you to his mother.

He said she had grown up in the 1950s “picking someone else’s cotton” in Georgia. Tonight, he said, she had “helped pick her youngest son to be a United States senator”.

Mr Walker did not explicitly concede as he took to the stage to address supporters at the College Football Hall of Fame in central Atlanta. But he said: “There’s no excuses in life, and I’m not going to make any excuses now because we put up one heck of a fight.” Mr Walker’s campaign was dogged by claims – which he denies – that he paid for two former girlfriends’ abortions, despite his calls for the procedure to be outlawed.

The 60-year-old also had to acknowledge during the campaign that he had fathered three children he had not mentioned publicly, after having long railed against absentee fathers. Republicans, meanwhile, ran an attack ad reminding voters of an allegation by Mr Warnock’s ex-wife that he ran over her foot in a car during a March 2020 domestic dispute.

Voting numbers in Georgia on Tuesday alone reached 1.4 million, election official Gabriel Sterling said after polls closed, adding there had been “record turnout across the board”. A record 1.9 million Georgians had already cast early or postal ballots.

Mr Warnock’s campaign enjoyed a big fundraising advantage, spending about $170m, compared with Mr Walker’s nearly $60m, according to federal filings.

Mr Walker’s Senate bid was the last Republican opportunity to flip a Senate seat after Trump-backed candidates lost in New Hampshire, Nevada, Arizona and Pennsylvania. Other Senate contenders Mr Trump championed won in Ohio, Wisconsin and North Carolina.