Video report by ITV News Correspondent Emma Murphy
George W. Bush has described President-elect Joe Biden as a "good man" and described the US election as "fundamentally fair".
In a statement, the former American leader said he congratulated Mr Biden and also Kamala Harris on her historic election to the vice-presidency.
Mr Biden clinched victory after winning the key battleground of Pennsylvania on Saturday – some four days after polls closed – pushing him over the 270 electoral college votes threshold.
Congratulatory messages have been sent by world leaders from across the globe over the past 24 hours - and now another former president has reached out personally.
He said: "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.
"The President-elect reiterated that while he ran as a Democrat, he will govern for all Americans.
"I offered him the same thing I offered Presidents Trump and Obama: my prayers for his success, and my pledge to help in any way I can."
Mr Bush said Donald Trump held the right to request recounts and pursue legal challenges as he congratulated him on his "hard-fought campaign".
The president was seen playing golf for the second day in a row and appears to show no sign of conceding the election soon.
In the statement he added: "He earned the votes of more than 70 million Americans - an extraordinary political achievement.
"They have spoken, and their voices will continue to be heard through elected Republicans at every level of government.
"The fact that so many of our fellow citizens participated in this election is a positive sign of the health of our democracy and a reminder to the world of its strength.
"No matter how you voted, your vote counted.
"President Trump has the right to request recounts and pursue legal challenges, and any unresolved issues will be properly adjudicated.
"The American people can have confidence that this election was fundamentally fair, its integrity will be upheld, and its outcome is clear."
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The president-elect has started work on a plan he hopes will help heal the United States.
He's set out four priorities - the battle against coronavirus, rebuilding the economy, racial justice and climate change.
He pledged late on Saturday to be a president that "seeks to unify" in his first speech as President-elect.
The Democratic candidate promised to be a president for all Americans, regardless of who they voted for, after he defeated Donald Trump in the race for the White House. Mr Biden told crowds in Delaware: “I’m humbled by the trust and confidence you’ve placed in me. “I pledge to be a president who seeks not to divide, but to unify. Who doesn’t see red and blue states, only sees the United States.
“And who will work with all my heart to win the confidence of all of you, and for that, I believe, is what America is all about.”