His son-in-law Jared Kushner and wife Melania have reportedly advised the Republican president to come to terms with President-elect Biden's victory while his adult sons pressed him and allies to keep fighting, CNN reported.

According to the report, Kushner, who is also President Trump’s senior adviser, has approached him to concede. The first lady, according to a separate source familiar with the conversations, has privately said the time has come for the president to accept the election loss.

Her first election-related tweet following Biden’s projected win said that she had told Trump to accept his loss, and that son-in-law Kushner had separately approached him about conceding.

On the other hand, Trump's two adult sons – Donald Jr and Eric – have urged allies to continue pressing on and they have pushed Republicans and supporters to publicly reject the results even as CNN and other news organisations projected the race for Biden on Saturday.

Trump push for legal challenges

The president, who was at his golf course in Sterling, Virginia, on Saturday and Sunday when the race was called, has not denied the outcome of the election privately even as he does so publicly, sources told CNN.

Trump is continuing to push his attorneys to pursue legal challenges that would delay formal certification of the results, and he has made no public indication that he is ready to accept the results of the election.

Trump asserted in a statement from his campaign – moments after CNN and other networks projected that Biden will become the 46th President of the United States – that Biden is "rushing to falsely pose as the winner" and that the race is "far from over."

Trump’s next line of action

"I will not rest until the American People have the honest vote count they deserve and that democracy demands," Trump said in the statement, which explains that the campaign's legal battle will begin Monday.

Biden campaign senior adviser Symone Sanders, told CNN's Jake Tapper on "State of The Union" Sunday that "a number of Republicans from the Hill have reached out," but said, "I don't believe anyone from the White House has."

Biden won the presidency Saturday after the battleground state of Pennsylvania pushed the Democrat over the 270 electoral votes needed to capture the White House.

White House chief of staff Mark Meadows, who recently tested positive for coronavirus, discussed next steps with the legal team Saturday.

Meanwhile, some members of Trump's party including Senators from South Carolina, Texas, Missouri on Sunday vocalised their opposition to the president conceding the election, urging him not to do so.

Trump's adult sons push for the fight

Trump's two adult sons have been key voices in urging President Trump and his allies to continue contesting the results of the 2020 election, according to multiple sources.

Beyond public posturing on social media, both Don Jr and Eric Trump have been digging in their heels, seeking to drum up broad GOP support for contesting the election results and telling allies they genuinely believe the election was fraudulent.

In recent conversations, Eric Trump has told allies he believes the election was "stolen from us," according to a source familiar with his comments, and vowed to fight to overturn the results.

The president has privately expressed frustration that some Republican leaders appear ready to move on from his race to focus on the Georgia election, people familiar with the conversations said, insisting they focus on him instead.