Obama is in Lima for an Asia-Pacific Economic Cooperation (APEC) summit that is likely to focus heavily on Trump's shock victory.
On Saturday, 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.
‘It's only been 10 days since the election,’ said US Trade Representative Michael Froman.
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.
‘But there are 11 other countries in TPP and I think that it is possible that they will agree to go ahead and pass TPP,’ he said in an interview, adding that they could ‘tweak’ the agreement to keep it alive without the US.
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.
Ahead of Obama's visit, National Security Advisor Susan Rice told AFP allies should expect those obligations to hold.
‘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.
But in the United States and throughout the West, there is growing opposition to deals that many say have contributed to jobs being sent overseas.
Obama is likely to make the case that globalization is a fact of life, and modern trade deals -- with sturdy environmental and labour provisions -- help shape that trend in the right direction.
- Nuclear Korea -
Obama is also slated to hold talks with Chinese President Xi Jinping on Saturday for a final meeting between the leaders of the world's two economic powers.
US officials say the sit-down will also deal with efforts to stop North Korea's ballistic missile and nuclear programs.
Obama is expected to press for an increase in the pace and severity of sanctions against North Korea, which is trying to develop a miniaturized nuclear warhead and a missile capable of delivering that deadly payload to the United States.
Beijing has long dragged its heels on sanctioning its allies in Pyongyang, fearing a flood of refugees if North Korea's economy collapses.
But earlier this year, Beijing moved to sanction a conglomerate based in China's frontier city of Dandong that had an estimated $530 million in trade with North Korea between 2011 and 2015.
