BEIJING—The U.S. and China made progress on narrowing their differences on trade issues, especially on purchases of U.S. goods and services and widening access to China’s markets, though the two sides are far from striking a deal.

In two intense days of talks in Beijing that will continue into Wednesday, U.S. and Chinese midlevel negotiators addressed a number of nettlesome issues and tried to specify how to ensure China will carry out pledges it made, according to people on both sides briefed on the discussions. The U.S....