Former US President George W Bush said the election outcome was "clear" while Trump refused to concede.
ADVERTISEMENTGeorge W Bush has become the highest-profile Republican to congratulate President-elect Joe Biden on winning the US presidential election.
The former US president said on Sunday that he had spoken with both Biden and Kamala Harris on the phone and offered his warm congratulations.
"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," Bush said.
Bush said that President Donald Trump had the right to request recounts and pursue legal challenges but that the "American people can have confidence that this election was fundamentally fair, its integrity will be upheld and its outcome is clear."
It came as President Trump continued to claim the election was stolen, with his campaign set on filing lawsuits over what they said were inconsistencies.
In particular, the campaign has alleged that Republican observers were not able to see ballot counting, when there are two observers from both parties present during vote counting which is video recorded.
Many Republicans have stayed silent on the election outcome as President Trump breaks from tradition and refuses to concede the election.
Senate Majority Leader Mitch McConnell, who said on Tuesday night that it was normal for courts to decide on election issues but that states do indeed run their own elections, has yet to issue a statement since the election result was called.
GOP Senator Roy Blunt told ABC News that he thought it was too early to declare Biden the President-elect but that a different outcome was "unlikely."
Some Trump allies have come to the president's defence, however, including Republican chairwoman Ronna McDaniel who tweeted: "The media doesn’t decide who wins elections, voters do. In multiple states the margins are razor thin with counting ongoing, several of which are headed for recounts."
Senator Marco Rubio also said that "the media can project an election winner" but do not get to decide if "claims of broken election laws & irregularities are true."
Trump ally Chris Christie took a different route, stating that Trump needed to show evidence of fraud.
"We can't back you blindly without evidence," Christie said.
Utah Senator Mitt Romney, the Republican candidate in 2012 who conceded to Barack Obama, was the first Senate Republican to congratulate Joe Biden.
In a statement, Senator Romney said President Trump was within his right to call for recounts but was "wrong to say that the election was rigged, corrupt and stolen".
He said Trump's claims damaged "the cause of freedom here and around the world, weakens the institutions that lie at the foundation of the Republic, and recklessly inflames destructive and dangerous passions."
Maryland Governor Larry Hogan also congratulated Joe Biden, calling for Americans to "come together."
Republican Senator Pat Toomey from Pennsylvania spoke out on Friday before the election result was called by news organisations.
ADVERTISEMENT"The president's allegations of large scale fraud and theft of the election are just not substantiated. I'm not aware of any significant wrongdoing here," the Pennsylvania Senator said.
Senator Toomey said counting took a long time in Pennsylvania due to a massive quantity of mail-in ballots.
In many of the states that took longer, mail-in ballots were not allowed to be counted until after the election.