President Obama on Wednesday promised a smooth transition to President-elect Donald TrumpDonald TrumpCaitlyn Jenner: 'I would seriously look at a run' for office Priebus: Syria, China moves part of 'Trump Doctrine' Poll: Most millennials disapprove of Trump MORE, as he called on Americans to stand behind their new leader and root for his success.

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"The presidency and the vice presidency is bigger than any of us," Obama said in the Rose Garden of the White House, flanked by Vice President Biden. 

“We are all rooting for his success in uniting and leading the country.”

Obama's remarks came less than half an hour after Hillary ClintonHillary Rodham ClintonPoll: Nearly 4 in 10 believe Trump campaign helped Russia meddle in election Dems crowd primaries to challenge GOP reps Dem: Pruitt violating anti-campaigning law with GOP fundraiser MORE's public concession speech in New York, in which she called on the nation to approach Trump's administration with an "open mind."

Obama congratulated Clinton on her campaign, calling her a role model to daughters across the country and predicting she and former President Bill Clinton will continue to do "great work." 

The president added that he was heartened by Trump’s remarks early Wednesday morning, in which he called for the country to come together. 

Obama and Trump are set to meet at the White House on Thursday. 

"It is no secret that the president-elect and I have some pretty significant differences,” Obama said. 

But he reminded Americans that the same was true about him and then-President George W. Bush in 2008, and he praised the previous administration for making that transition a smooth one. 

"So I have instructed my team to set the example that President Bush’s team set eight years ago, and work as hard as we can to make sure this is a successful transition for the president-elect,” the president said. 

Trump's surprise victory over Clinton stunned the political world, an outcome few had predicted even as the polls began to close. 

It served as a direct repudiation of Obama, who had cast Clinton as a guardian of his legacy as he campaigned for her, and the morose feelings at the White House were palpable. 

Dozens of shellshocked staffers filed into the Rose Garden to watch the statement, including Valerie Jarrett, Denis McDonoughDenis McDonoughSunday shows preview: McMaster hits circuit for second straight week Obama chief of staff: 'The president cannot order a wiretap' Obama's chief of staff joins foundation with focus on jobs MORE and Susan Rice — all members of the president’s inner circle. 

There were many hugs and people leaning their heads on others’ shoulders. White House press secretary Josh Earnest was spotted consoling a crying staff member before the president’s remarks began. 

Yet, Obama sought to project a positive image for the nation. 

He told his team to keep their "heads up," lauding the "remarkable work [that] has left the next president with a stronger, better country than the one that existed eight years ago."

"I think of this job as being a relay runner,” the president said, veering off-script from his prepared remarks. “You take the baton, you run your best race and, hopefully, by the time you hand if off, you are a little further ahead, you made a little progress. I can say that we’ve done that.”

Teary-eyed staffers gave the president a lengthy Rose Garden ovation that continued even after he and Biden returned to the Oval Office. 

Despite animosity between himself and the president-elect — Trump spent years questioning Obama’s citizenship and his eligibility to serve as president, an attack the president’s allies said was racially motivated — Obama framed the contentious election as an "intramural scrimmage" between friends. 

"We are not Democrats first; we are not Republicans first. We are Americans first. We are patriots first. We all want what’s best for the country," Obama said. 

"That’s what I heard in Mr. Trump’s remarks last night. That’s what I heard when I spoke to Mr. Trump last night, and I was heartened by that. That’s what the country needs — a sense of unity, a sense of inclusion, a respect for our institutions, our way of life, rule of law, and respect for each other."