At the heart of Trump’s latest trade deal with Vietnam and talks with other trading partners is an effort to counter what he sees as China’s unfair practices to circumvent U.S. tariffs.

The US trade agreement with Vietnam reportedly lowers tariffs but lacks detail, triggering sharp warnings from Chinese officials.

SINGAPORE—A tariff agreement with Vietnam emphasizes one of the White House’s top priorities in this frantic round of dealmaking over global trade: Slamming shut any back door routes for Chinese goods to enter the U.