SEOUL—American and South Korean captains of industry gathered in a convention center here to mark the fifth anniversary of the U.S.-South Korean trade pact. But it was a nervous celebration.

Many on Wednesday were worried the U.S. will try to renegotiate or even abrogate the hard-fought agreement, which many tout as “the gold standard,” after U.S. President Donald Trump deemed it detrimental to American interests. Mr. Trump already scrapped American participation in the Trans-Pacific Partnership, which was structured on the...