BEIJING—The U.S. and China opened talks on Monday to resolve a trade fight that is threatening the global economy, with U.S. negotiators focused on a make-or-break issue: guarantees that Beijing will follow through on its offers.

The negotiations, which run through Tuesday, are the first time the two sides have met face-to-face since President Trump and President Xi Jinping of China agreed to a temporary tariff truce during a meeting in Argentina on Dec. 1. Mr. Xi’s top economic policy aide stopped by the meeting to greet...