President Donald Trump's inner circle is beginning to split over his ongoing refusal to accept the results of the 2020 election, as Jared Kushner and first lady Melania Trump advised him to come to terms with President-elect Joe Biden's victory and his adult sons pressed him and allies to keep fighting. 

Kushner, the President's son-in-law and senior adviser, has approached him to concede, two sources told CNN. The first lady, according to a separate source familiar with the conversations, has privately said the time has come for him to accept the election loss.

Meanwhile, 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 organizations projected the race for Biden on Saturday.

Trump's campaign is planning a messaging blitz to fuel its argument -- unsupported by any evidence to date -- that the President's second term is being stolen from him through corrupt vote counts in battleground states, three sources familiar with the matter told CNN on Sunday evening.

Trump campaign spokesman Jason Miller in a tweet Sunday morning denied that Kushner has approached Trump, although CNN stands by its reporting.

"This story is not true," said Miller. "Jared has advised @realDonaldTrump to pursue all available legal remedies to ensure accuracy."

Meanwhile, some members of Trump's party on Sunday vocalized their opposition to the President conceding the election, urging him not to do so.

Republican Sen. Lindsey Graham of South Carolina, one of the President's closest allies in the Senate, said "the President should not concede" during an interview on Fox News.

Texas Sen. Ted Cruz, who was also Trump's one-time primary rival, also advised against concession, saying it would be "premature."

And Sen. Roy Blunt of Missouri, a member of Republican leadership in the Senate, would not acknowledge on Sunday that Biden is the President-elect, citing both the legal challenges initiated by Trump's lawyers in states across the country and the ongoing vote counting process as reasons.