Trade ministers said they had agreed on “core elements” of a revised version of the Trans-Pacific Partnership without America, a deal that still brings together Japan, Mexico and Australia and a host of other countries with a combined GDP of more than $10 trillion.

An agreement would be a win for countries advocating a multilateral trading order at a time when Mr. Trump is pushing for bilateral deals and protectionism is rising globally. It would also provide a counterweight to rising Chinese influence in Asia and give the participants greater bargaining power in seeking other trade deals. Trade experts say that even without the U.S., the income gains could total more than $150 billion annually for members. Negotiators say they have left the door open for the U.S. to re-enter the pact at a later date, if desired.