Standing next to German Chancellor Angela Merkel in Berlin, Obama said Trump would quickly see that a president's responsibilities can't be treated casually and that diverse countries can only be governed by "listening and reaching out."
"It is my hope that that is what will happen," Obama said. "And I'm going to do everything I can over the next two months to help assure that that happens."
Though the outgoing president made clear his profound disdain for Trump throughout the campaign, perhaps no one is better positioned than Obama to get him up to speed in a matter of weeks.
It's unclear, though, how much help Trump wants or will accept from Obama. And no one expects that the executive tutoring will substantially change Trump's vast differences with Obama, who he called the worst president in U.S. history.
After meeting with Trump following the election, Obama resolved to spend more time helping prepare Trump than he might under different circumstances — say, if Hillary Clinton had been elected, aides said.
Trump, to the surprise of many, seemed game. He said he wanted Obama's "counsel" and looked forward to "many, many" more meetings.
In the run-up to the election, the White House had planned only perfunctory, refresher-style briefings for Clinton, who is no stranger to the White House and whose transition team had prepared extensively for an expected takeover.
Soon after Trump's victory, White House chief of staff Denis McDonough directed that his preparatory materials be thickened and his intelligence briefings expanded to include more basic information, according to U.S. officials, who weren't authorized to discuss the matter publicly and requested anonymity.
Obama and his closest advisers were irritated when it leaked out that Trump, during his White House visit, had displayed a lack of thorough knowledge about key issues while Trump's aides appeared unfamiliar with the process of staffing up a White House, officials said.
They were concerned if Trump felt insulted or aggrieved, he might pull the plug on accepting Obama's advice and help. After all, Obama's aides had been pleasantly surprised when Trump, after their Oval Office chat, had agreed to preserve key elements of the "Obamacare" health law, which he'd pledged during the campaign to repeal.
If Trump has felt patronized by Obama, so far he hasn't shown it. Asked why Trump's meeting this week with Japanese Prime Minister Shinzo Abe was closed to the press, senior transition adviser Kellyanne Conway pointed out that Obama was traveling overseas.
"We are very deferential and respectful of the fact that we already have a president of the United States, Barack Obama," Conway told reporters. "President Obama is still in office for the next two months, and we won't be making diplomatic agreements today."
Though Trump and Vice President-elect Mike Pence have spoken by phone to more than 30 heads of state since the election, Trump hasn't been heard from publically, save for one television interview and occasional tweets. From his suite in Trump Tower, he and top aides have been interviewing candidates for the 4,000-odd roles they must fill.
Unsure how Trump as president may shake up foreign relations, world leaders have turned to Obama for information about what to expect. Traveling this week to Greece, Germany and Peru, Obama has tried to reassure U.S. partners that Trump, in their Oval Office meeting, expressed a "full commitment" to NATO.
"I am encouraged by the president-elect's insistence that NATO is a commitment that does not change," Obama said in Germany.
During the campaign, Trump said the U.S. didn't "really need NATO in its current form," calling it obsolete and threatening not to defend NATO allies unless they pay more into the alliance. Though Trump has since softened those comments, he hasn't offered the explicit reassurances in public that Obama said he offered in private.
But Obama said he was "cautiously optimistic" that transitioning from candidate to president-in-waiting would force Trump to focus and get serious about "gaining the trust even of those who didn't support him."
"That has to reflect itself not only in the things he says, but also how he fills out his administration," Obama said. "And my hope is that that's something he is thinking about."
Reach Josh Lederman on Twitter at http://twitter.com/joshledermanAP