Chris Christie: Donald Trump and I haven't discussed a potential Cabinet role

New Jersey Gov. Chris Christie says he and President-elect Donald Trump "have not talked about anything" related to a potential Cabinet appointment within the new administration.

"The president-elect was absolutely adamant about not discussing the transition before he was elected," Christie told Matt Lauer and Savannah Guthrie in an exclusive interview Thursday.

Christie, who has been leading Trump's White House transition team, has served as an adviser to the president-elect ever since he dropped out as a candidate in the Republican presidential primary season.

Related: Trump and Christie on the campaign trail

Christie's early endorsement of Trump was seen as shocking at the time, given how critical he was of the real estate developer-turned-reality show star when the two were rivals. But the gamble paid off following Trump's surprise Election Day victory over Hillary Clinton.

Christie said he and Trump spoke on election night, "but we didn't speak about me, we spoke about the transition."

Asked specifically whether he'd like to serve as Trump's chief of staff or attorney general, Christie refused to answer.

"I have a job do to help get the administration ready. If there's some role for me that I want to do, and that the president-elect wants me to do — we've known each other for 14 years — we'll talk about," he said, then adding, "Maybe it's host of the TODAY show, Matt. Who knows."

Trump's upset win prompted a wave of demonstrations across the country Wednesday, with many protesters chanting "Not my president" and expressing concern over how their new president may target minority groups like he did during his campaign.

Trump will have a White House meeting Thursday with President Obama, who has campaigned as recently as days ago against the Republican candidate and has labeled him as "unfit" for office. But during a statement he delivered Wednesday, Obama pledged to ensure a smooth transition to a Trump administration.

"We are now all rooting for his success in uniting and leading the country," he said.

The president's remarks came shortly after Clinton delivered a concession speech expressing hope that Trump will be "a successful president for all Americans," acknowledging a deeply divided nation.

"We owe him an open mind and a chance to lead," she said.

Christie acknowledged the adversarial relationship Obama has had with Trump, who started the "birther movement" that questioned whether the president was actually born in this country but said, "I think that's all past us" and dismissed the tension to "politics."

"What these two men recognize is that now this is about governing and leading the nation and the world," he said. "And they have a lot more important things to talk about besides slights, real or perceived in the past."