The 12-nation Trans-Pacific Partnership covered 40 percent of the global economy before Trump abruptly abandoned it in January as part of a campaign pledge to save American jobs he says have been sucked up overseas.
But key remaining members of the pact are desperate to keep the deal alive, believing it will lock-in free trade as well as boost labour rights and environmental protections.
The charge is being led by Japan, New Zealand and Australia who are leading the so-called TPP 11.
After an early morning huddle in Hanoi, New Zealand Trade Minister Todd McClay told reporters that the TPP 11 "are committed to finding a way forward to deliver" the pact.
Trade representatives agreed to help the United States to rejoin the deal at any time, pinning hopes on a U-turn in American policy.
"We very much expect the full participation of all countries that negotiated TPP from the start, and we will consider a mechanism to ensure (that)," said Vietnam's Trade Minister Tran Tuan Anh, who co-chaired the meeting.
Spearheaded by former US president Barack Obama, the far-reaching TPP -- which notably excludes China -- would have rewritten the rules of 21st century trade.
The deal goes further than most existing free trade pacts, with labour laws, environmental protections and intellectual property rights touted as a new gold standard for global trade.
It promised to transform smaller economies such as Vietnam by carving out unprecedented access to the world's top economies.
But Trump denounced the deal as a "job killer" and a "rape" of American interests.
His administration has instead vowed to seek bilateral trade deals with partners.
Balance of power
The deal was also seen as a way to counter Beijing's regional economic dominance.
Reviving the TPP, even without the heft of the world's biggest economy, would still provide ballast against China, analyst Alex Capri told AFP.
"The Chinese would not be particularly pleased to see the TPP go ahead even without the United States," said Capri, a senior fellow and professor at the National University of Singapore.
He did not rule out the eventual return of the United States to the TPP, noting that Trump has "flip-flopped" on other campaign positions in a headline-grabbing first few months in office.
The TPP ministers met on the sidelines of a gathering of trade ministers from the Asia-Pacific Economic Cooperation (APEC) in preparation for a November summit of global leaders.
Newly-appointed US trade chief Robert Lighthizer attended the two-day gathering, where he was scheduled to meet one-on-one with several ministers, including from China, Canada and Mexico.
The Reagan-era trade veteran has been tasked with renegotiation of the North American Free Trade Agreement (NAFTA) -- another deal Trumped promised to pull out of, though he later backpedalled after speaking to the leaders of Canada and Mexico.
The Trump administration has said it is seeking bilateral agreements over sweeping free trade pacts, and is pushing for fair trade with partners, not just free trade.
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