Obama is in Lima for an Asia-Pacific Economic Cooperation (APEC) summit that is likely to focus heavily on Trump's shock victory.
Today, he will meet leaders of the 12-country Trans- Pacific Partnership, or TPP, which Trump has opposed and now faces an uncertain future.
White House officials admit the chances of passing the deal are slim, but Obama will urge leaders to give the new president time to formulate policy.
From Obama down, officials have stressed that US economic and strategic interests have not changed as a result of the election, and Trump may yet recalibrate his views.
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He warned of "serious" strategic and economic costs if the United States walks away from the deal, designed to be a cornerstone of US influence in the Asia-Pacific region.
But there is little chance of Trump's Republican allies in Congress ratifying TPP anytime soon.
"I think that is a real blow to US interests, economically and strategically, in terms of our position in Asia, but I think that is the reality, that the US is not going to be participating," said Matthew Goodman, an expert on Asian economics with the Center for Strategic and International Studies.
Some allies are turning their attention to a rival Chinese-backed free trade agreement.
Japanese leader Shinzo Abe, who took domestic political risks to back the US trade deal, visited Trump in New York on Thursday to hear from the president-elect himself.
Trump has sparked concern in Japan and South Korea in particular by questioning decades-old mutual defense obligations that underpin their security.
"It is manifestly in the United States's interests for these alliances to endure and to be a source of confidence to our partners and for them to understand that they don't need to come out from under the US umbrella," she said.
While stressing that she did not want to speculate about Trump's foreign policy, she sought to reassure key US allies in NATO and the Pacific Rim that they will not be abandoned.
Many Pacific nations are clamoring for deeper trade ties with the rest of the world.
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