Former Republican US president George W Bush said on Sunday he had spoken to president-elect Joe Biden, a Democrat, to congratulate him on his victory.
Mr Bush said Americans could have confidence in the US vote, which took place last Tuesday but was called in Mr Biden's favour on Saturday.
"Though we have political differences, I know Joe Biden to be a good man who has won his opportunity to lead and unify our country," Mr Bush said.
"The American people can have confidence that this election was fundamentally fair, its integrity will be upheld, and its outcome is clear."
He said that defeated President Donald Trump had "the right to request recounts and pursue legal challenges".
Twenty years ago, Mr Bush's presidential race against Democrat Al Gore was decided after a Supreme Court decision to halt a recount in Florida.
The statement by the only living Republican former president made him one of the country's most prominent party members to acknowledge Mr Biden's victory.
His brother Jeb, the former Florida governor who had aspired to the presidency until Mr Trump won the party's nomination in 2016, earlier sent Mr Biden his congratulations.
"I will be praying for you and your success," Jeb Bush said.
"Now is the time to heal deep wounds. Many are counting on you to lead the way."
Republican senators Mitt Romney of Utah and Lisa Murkowski of Alaska have also extended their congratulations to Mr Biden.
But many other Republican officials are calling that premature, saying not all votes have been counted and not all challenges resolved.
