U.S. talks with China to complete a first-stage trade deal had hit an impasse around Thanksgiving, raising fears a nascent accord would collapse again—and with it, hope for a halt to the nearly two-year-old trade war.

Looking for a direct route to the president, Chinese Ambassador Cui Tiankai spoke with President Trump’s son-in-law and adviser, Jared Kushner, say people familiar with the episode. The U.S. offer didn’t roll back enough tariffs, he told Mr. Kushner.

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