But in his first news conference since last week's stunning election results, Obama warned that some of Trump's expectations will soon be shaken up by the gravity of the job.
Obama said he was certain after meeting Trump last week that his successor and longtime political foe was "sincere" about being president for all Americans but also called on the President-elect to reach out to people who felt anxious after the explosive rhetoric of the campaign, including women and minorities.
"I don't think he is ideological, I think ultimately he is pragmatic in that way and that can serve him well as long as he has got good people around him and he has a good sense of direction," Obama said.
Obama appeared before reporters before leaving the United States on the last scheduled foreign trip of his presidency, to Greece, Germany and Peru. It takes place with many of Obama's subordinates and liberals across the nation still barely able to believe he will be succeeded by Trump, whose volatile character and taboo-busting rhetoric could hardly strike a more overt contrast to the current president.
Obama said he told Trump that his election achievement in tapping into the enthusiasm of his voters was impressive.
"I think he is coming to this office with fewer set hard and fast policy prescriptions than a lot of other presidents might be arriving with. Do I have concerns? Absolutely, of course I've got concerns. He and I differ on a whole bunch of issues," Obama added.
Obama dodged an opportunity to comment on the appointment of firebrand polemicist Stephen Bannon as Trump's senior White House policy adviser, who has been vigorously criticized as a leading member of the alt-right nationalist movement.
Obama said it would not be appropriate for him to weigh in on all of Trump's appointments because it would be incompatible to his desire to provide a smooth transition of power to his successor.
"I think it is important for us to let him make his decisions. The American people will judge over the course of the next couple of years whether they like what they see," Obama said.
He added: "This office has a way of waking you up. Those aspects of his positions or his predispositions that don't match up with reality, he will find shaken up pretty quick because reality has a way of asserting itself."
Obama was repeatedly pressed about Trump's temperament, which he had criticized extensively during the campaign.
"There are going to be certain elements of his temperament that will not serve him well unless he recognizes them and corrects them," Obama said, pointing out the impact that a comment from a US president that is not accurate can have around the world.
"I think he recognizes that this is different," he said.
Affirms US commitment to NATO
Obama also said Monday that the United States would remain the world's "indispensable" power and that Trump had told him he was committed to NATO.
"In my conversations with the President-elect, he expressed a great interest in maintaining our core strategic relationships," Obama said, adding that he had a message from Trump to pass on to world leaders he will meet this week. "One of the messages I will be able to deliver is his commitment to NATO and the transatlantic alliance."
The President said that there were many diplomatic, military and humanitarian levers of US power that made America the indispensable nation in the world and that status would continue.
"There is no weakening of resolve when it comes to maintaining a strong and robust NATO relationship," Obama said.
Obama had hoped to be handing the reins to a fellow Democrat Hillary Clinton, yet is now preparing the way for Trump, a man for whom he has harbored personal and political animosity, and who has pledged to tear up his legacy as quickly as possible.
Obama, who met Trump in the White House for 90 minutes Thursday, stressed to reporters the importance of a smooth transition process, similar to the one he was offered by former President George W. Bush.
He said the most important point he made to Trump was the importance of setting up a proficient staffing structure, including the chief of staff, national security adviser and White House counsel.
"I hope it was useful," Obama said. "I hope that he appreciated that advice."
He said he told Trump that "gestures matter" and how he reaches out to groups that did not support him were important.
"I think it is important to give him the room and the space to do that, it takes time," Obama said.
Trump may be in more need of assistance than other recent presidential election winners, considering he has no experience whatsoever of governing yet is about to take on what may be the world's toughest job.
Some White House staffers were surprised by the businessman's rudimentary grasp of White House operations but say they will work to get the new administration up to speed before January 20.
Officials described Trump's visit as a wake-up call of sorts, revealing the work to be done with the new White House staff before Trump is sworn in.
Obama argued Monday that despite there being some "deeply disaffected" people, the country he will turn over to Trump is in better shape than it was in when he took office in 2009, amid the worst financial crisis since the Great Depression.
He said that economic indicators including unemployment were as healthy as they had been in years, and despite challenges in the Middle East, the US was in a strong position against ISIS.