WATCH: President Obama On Trump Win, Clinton Loss

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President Obama, saying "we are all rooting for his success," vowed his staff would work as hard as it can to ensure a successful transition of power to president-elect Donald Trump.

Obama spoke in the White House Rose Garden with Vice President Joe Biden at his side. The president had phoned Trump at 3:30 Wednesday morning to congratulate him on his upset victory over democrat Hillary Clinton, and invited Trump to the White House Thursday to discuss transition matters.

Obama said it is no secret that he and Trump have "pretty significant differences." But Obama said he and former President George W. Bush had significant differences too, but still had a smooth transition after Obama's election in 2008.

Later White House spokesman Josh Earnest, asked whether the president would take steps to protect some of his policies, including the nuclear agreement with Iran and the Affordable Care Act before leaving office, responded that Obama would still be President until January 20th.

Obama spoke minutes after Clinton formally conceded defeat to Trump after an often-bitter campaign. Obama said he "couldn't be prouder" of Clinton, whose candidacy and nomination he called historic, and which "sends a message to our daughters all across the country that they can achieve at the highest levels of politics."

Obama said what he heard from Trump in a private conversation and in the president-elect's public remarks was that "we all want what's best for our country." Obama said that what the nation needs, a sense of unity, a sense of inclusion and respect for our institutions our rule of law and "respect for each other."

The president said that "everybody is sad when their side loses an election, " but that we're all actually on the same team, calling elections an intermural scrimmage. He said he told his staff "to hold their heads up," that their "remarkable work has left the next President with a stronger, better country that the one that existed eight years ago."