It worries that companies that have moved much of their supply chains to China could make components there, ship them to a member of the Trans-Pacific Partnership for assembly, then sell them in the United States tariff-free.
There is also skepticism from other countries in the 11-nation deal: Australia's trade minister says there's very little appetite for a renegotiation, and Japan's minister on the file compares the deal to a carefully crafted glass sculpture that would be hard to change. Malaysia's International Trade and Industry Minister Mustapa Mohamed echoed these remarks, saying that renegotiation would "alter the balance of benefits for parties".
Larry Kudlow, Trump's top economic adviser, said in an interview on Thursday with The New York Times that the request to revisit the deal was somewhat spontaneous.
Trump, in his earlier tweet, said the U.S. "would only join TPP if the deal were substantially better than the deal offered to President (Barack) Obama".
Trade Minister Steve Ciobo says the 11 nations behind the Trans-Pacific Partnership hope to finalise the trade deal by early 2019.
Comparing the multicountry trade agreement to "a glasswork", Yoshihide Suga, Japan's chief cabinet secretary, cautioned against any efforts to change it to accommodate Trump. Trump has warned that he could levy tariffs on $150 billion in Chinese goods, prompting Beijing to threaten retaliatory measures aimed at American soybeans, airplanes and other products.
The agreement partners had little appetite for substantial negotiation, but would welcome the U.S. coming back to the table for further talks, he said. "I think they want to".
The remarks were another conciliatory signal from the administration following tit-for-tat tariffs proposals from the world's largest two economies that rattled markets. Asian stocks climbed as equities in Japan and Australia advanced.
Trump's decision to withdraw from the TPP was among his first actions after he was inaugurated in 2017. It would give the pact a great deal more heft and help position it as an economic counterweight to China, which increasingly dominates the Asia-Pacific region.
Trump says that last Saturday, Syrian President Bashar Assad deployed chemical weapons in what was a "significant escalation in a pattern of chemical weapons use by that very bad regime".
Aso said he expected Prime Minister Shinzo Abe and Trump to discuss the trade deal at their summit meeting next week.
The barriers to a new pact are considerable. AFL-CIO President Richard Trumka, head of the main trade union group, said on Twitter that TPP "was killed because it failed America's workers and it should remain dead".
The 11 remaining nations represent 13% of global output and include Japan and Canada.