US President Donald Trump has defeated President-elect Joe Biden in Alaska, Edison Research projected, while Republican Senator Dan Sullivan won re-election in the same state.

Mr Trump has yet to concede the presidential election four days after Edison Research and major TV networks said Mr Biden had surpassed the 270 Electoral College votes needed to capture the presidency.

Awarding Alaska's three Electoral College votes to Mr Trump will not change the outcome of last week's election.

Mr Sullivan’s victory gives his party exactly half of the Senate's 100 seats with two races outstanding.

Winners of two Senate seats in Georgia are to be decided in January runoffs.

If Democrats win the two Georgia races, the tie-breaking vote in the evenly divided Senate will be held by Kamala Harris, vice president-elect.

Meanwhile, Mr Biden will further lay the groundwork for his new administration today as President Trump pursues a flurry of long shot lawsuits challenging the election results in an effort to cling to power.

Mr Trump has declined to concede, instead lodging unsupported charges of election fraud that have gained little traction.

Judges so far have thrown out lawsuits in Michigan and Georgia brought by Mr Trump's campaign, and legal experts say the litigation has little chance of changing the outcome of the election.

Nearly 80% of Americans, including half of Republicans, say Mr Biden is the rightful winner, according to a Reuters/Ipsos poll released yesterday.

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Jill and Joe Biden at a veterans day event in Philadelphia

Mr Trump's refusal to accept defeat, even as world leaders congratulate Mr Biden and look to their future relations, caps a tumultuous four years in office with the US deeply polarised, ravaged by the coronavirus and torn by racial division.

But Mr Trump's supporters, who as of the latest count gave him more than 72 million votes compared to Mr Biden's 77 million, have delighted in his combative style and shattering of norms.

President Trump has eschewed a public concession or the pledge of cooperation typically offered by outgoing presidents.

"It's an embarrassment, quite frankly," Mr Biden told reporters yesterday. "How can I say this tactfully? I think it will not help the president's legacy."

Mr Trump's fellow Republicans have largely stuck with him, saying he has a right to contest the result.

Texas Lieutenant Governor Dan Patrick said he would pay up to $1m from his campaign account to people who come forward with evidence of voter fraud.

But privately, some say Mr Trump must soon produce significant evidence or exit the stage.

Senator Rob Portman of Ohio, a state that Mr Trump won handily last week, said that Mr Biden is leading in enough states to win election "and President Donald Trump's campaign must produce evidence to support allegations of election fraud".

Mr Portman added that he hoped states and courts would move "expeditiously" to resolve the matter.

President Trump suffered another possible setback yesterday when Democrats on the House of Representatives Oversight Committee said a postal worker who claimed he witnessed ballot tampering in Pennsylvania had recanted his allegations, according to the Postal Service's internal watchdog.

Biden preparing to govern

Mr Biden plans to meet advisors today who are helping him prepare to take office on 20 January 2021.

He has tapped finance, trade and banking regulation experts for his transition team that range from core Democrats to progressive activists, reflecting ongoing debate within the party about how to address climate change, wealth inequality and other issues.

Mr Biden is also tapping people who crafted tougher environmental rules while serving under President Barack Obama.

Mr Biden secured the presidency on Saturday after television networks concluded he had won Pennsylvania and Nevada, giving him 279 Electoral College votes, more than the 270 needed to take the White House.

The outcome is still undecided in several states with Mr Trump holding a lead in North Carolina and Mr Biden ahead in Georgia and Arizona.

Recounts are expected in several states, though they are unlikely to change the outcome.

Nationwide, Mr Biden is leading Mr Trump by 3.2% or nearly 5 million votes as final tabulations trickle in.

In order to remain in office, Mr Trump would need to win all three undecided states plus overturn the results in one or more states already in Mr Biden's column.

Donald Trump salutes at the Tomb of the Unknown Soldier at Arlington

Meanwhile, Mr Trump has placed a memorial wreath at the Tomb of the Unknown Soldier in Arlington National Cemetery to mark Veterans Day.

It was his first public appearance, other than two golf outings, since an angry White House news conference last Thursday.

The Trump administration is not cooperating with Mr Biden’s team, which has been unable to move into federal government office space or tap funds to hire staff.

US Secretary of State Mike Pompeo yesterday predicted a "second Trump administration," in comments at odds with congratulatory phone calls from the leaders of Britain, France, Germany and Ireland to Mr Biden.

Mr Trump has installed loyalists in top positions at the Pentagon, one day after firing Defense Secretary Mark Esper, which could potentially make it easier to use US troops to respond to domestic protests.