BEIJING—China’s chief trade negotiator has invited his American counterparts for a new round of face-to-face talks, according to people briefed on the matter, as both sides are struggling to strike a limited deal to help de-escalate tensions between the world’s two largest economies.

During a phone call late last week, Liu He, President Xi Jinping’s point person on trade negotiations with Washington, extended the invitation to U.S. Trade Representative Robert Lighthizer and Treasury Secretary Steven Mnuchin to hold the meeting...