BEIJING—The U.S. and China wrapped up their first face-to-face trade negotiations since a temporary tariff truce was declared last month, making progress toward an agreement but leaving the thorniest issues to be resolved in higher-level talks, according to people with knowledge of the discussions.

During three days of talks between midlevel trade officials from Washington and Beijing in the Chinese capital that ended Wednesday, the two sides made progress on issues such as additional Chinese purchases of U.S. goods and services, as well as opening China’s markets further to American capital, the people said. But they cautioned that the two teams hadn’t yet made a breakthrough and more discussions are needed to resolve a trade fight that has unnerved global markets.

The two sides remain divided on knottier issues including a reduction of Chinese subsidies to domestic firms and protection of intellectual property, the people said, and that means a resolution still needs to be hammered out. The U.S. delegation, led by Deputy U.S. Trade Representative Jeffrey Gerrish, left Beijing late Wednesday afternoon.

In a statement released after talks concluded, the trade representative’s office said officials had discussed making any deal “subject to ongoing verification and effective enforcement.” The statement added that negotiators had “conveyed President Trump’s commitment to addressing our persistent trade deficit and to resolving structural issues in order to improve trade between our countries.”

In a brief statement issued Thursday morning, China’s Commerce Ministry said the three-day negotiations “promoted mutual understanding and laid the foundation for solving problems of mutual interest.” It also said both sides had agreed to keep close contact.