Former Republican US president George W Bush has said that the American people can have confidence that the 2020 presidential election was "fundamentally fair, its integrity will be upheld, and its outcome is clear".

Bush, however, also said that outgoing President Donald Trump has the right to request recounts and pursue legal challenges, with any unresolved issues to be properly adjudicated.

In a statement after speaking to President-elect Joe Biden over phone, Bush said he extended his warm congratulations to Biden and thanked him for the patriotic message in his national address after being declared the election winner.

Bush, 74, who was the US president from 2001 to early 2009, said that while he and the 77-year-old Democrat leader have political differences, he knows Biden to be 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,” he said.

Bush, as president and Biden then as chairman of the Senate Foreign Relations Committee, had worked together on a number of issues during the Bush administration including the India-US civil nuclear deal.

Bush also called Vice President-elect Kamala Harris to congratulate her on her "historic" achievement.

Bush in his statement also congratulated Trump and his supporters on a hard-fought campaign. "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," he said.

Trump has not conceded losing to Biden and filed numerous lawsuits claiming irregularities cost him re-election to a second four-year term.

"The fact that so many of our fellow citizens participated in this election is a positive sign of the health of America's democracy and a reminder to the world of its strength," he said.

No matter how you voted, your vote counted," he said.

"The American people can have confidence that this election was fundamentally fair, its integrity will be upheld, and its outcome is clear, Bush said.

The challenges that face our country will demand the best of President-elect Biden and Vice President-elect Harris and the best of us all. We must come together for the sake of our families and neighbours, and for our nation and its future, he said.

"There is no problem that will not yield to the gathered will of a free people," Bush said.

Democrat Biden has defeated Trump to become the 46th president of the United States after a bitter and closely-fought presidential election - billed as one of the most divisive in recent American history.

With this all four living previous presidents of the United States Jimmy Carter, Bill Clinton, Barack Obama and George Bush -- have congratulated Biden and Harris on their historic election.

“Rosalynn joins me in congratulating our friends President-elect Joe Biden and Vice President-elect Kamala Harris. We are proud of their well-run campaign and look forward to seeing the positive change they bring to our nation,” Carter said in a statement.

Obama spoke separately with President-elect Biden and Vice President-elect Harris on Saturday. He congratulated each of them on their historic victory and told them how proud he was of the campaign they ran in unprecedented times, his spokesperson said.

“America has spoken and democracy has won. Now we have a President-Elect and Vice President-Elect who will serve all of us and bring us all together. Congratulations to Joe Biden and Kamala Harris on your momentous victory!” Clinton said in a tweet.

PTI