President Donald Trump, fed up with hearing he was weak on China, assembled his senior trade team at the White House on May 22 and vented, according to officials who were involved. He wanted a tougher approach, including tariffs he could use as a weapon to force trade concessions.

Treasury Secretary Steven Mnuchin, who favored a milder approach, had spent months maneuvering to become the administration’s point person on talks with China. Now, along with his administration rivals, he was getting a dressing down, the officials...