Its new deal with Vietnam and its fresh tariff threats issued to many other countries seem designed to reduce China’s role in their supply chain. Countries that had hoped to stay out of the new cold war now fear they are being forced to pick a side. To appease the world’s biggest market, they must anger the world’s biggest trader.

WASHINGTON—President Trump reignited his global trade war Monday, renewing his threat to hit partners with punishing tariffs even as he announced a three-week extension to negotiate deals. Trump signed an executive order extending the date when his so-called reciprocal tariffs would take effect,