Jared Kushner has approached President Trump about conceding the election

'I will not rest until the American People have the honest vote count they deserve and that Democracy demands,' Trump had said in a statement

Jared Kushner, Donald Trump's son-in-law and senior adviser, has approached the President about conceding the closely-fought election to his Democratic rival Joe Biden, according to media reports on Sunday.

The move comes following Trump's assertion in a statement from his campaign -- after major US media outlets projected that President-elect 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."

Kushner has approached the President about conceding the election, CNN quoted two unidentified sources as saying.

Kushner has told others that he has urged the president to accept the outcome of the race — even if Trump won't come to terms with how it was reached, the Associated Press also reported on Sunday.

Read | Top Republicans are silent on Joe Biden victory as Donald Trump refuses to concede

"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 states that the campaign’s legal battle will begin Monday.

Biden-Kamala Harris deputy campaign manager Kate Bedingfield said that there has been no communication between Biden and Trump, or between any representatives from either campaign, since the race was called earlier in the day after the 77-year-old former US vice president crossed the 270 electoral college votes required to win the race for the White House.

Biden, in his victory speech on Saturday night, did not mention Trump, a Republican, by name.

Biden said he was humbled by the trust America had placed in him and reached out to those Americans who did not vote for him.

"I understand the disappointment tonight. I've lost a couple of times myself. But now, let's give each other a chance," he said, adding later in his remarks, "This is the time to heal in America."

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Biden claimed that he would be a president that would lead the entire nation, regardless of political party.

“I pledge to be a president who seeks not to divide but unify — who doesn’t see red states and blue states, only sees the United States,” Biden said.

The former vice president noted in his remarks that it is time both sides "listen to each other again."

"It's time to put away the harsh rhetoric, lower the temperature, see each other again, listen to each other again, and to make progress, we have to stop treating our opponents as our enemies. They are not our enemies. They are Americans," Biden said.