WASHINGTON—President Trump overruled advisers to ramp up tariffs on China after a heated exchange in which he insisted levies were the best way to make Beijing comply with U.S. demands, according to people familiar with the matter.

Barring a break in the impasse, the U.S. is now poised to impose 10% tariffs on roughly $300 billion in Chinese imports that aren’t currently taxed starting Sept. 1. Battle lines are hardening in Beijing as well—raising prospects that a deal may be put off until after the U.S. presidential election next year.

Mr. Trump, who has speculated the Chinese may be waiting to negotiate with a possible Democratic successor, says a strong U.S. economy gives Washington the upper hand if the dispute drags on. But advisers argued that a new round of tariffs could hurt the U.S. economy and further strain relations with China.

Trade talks in Shanghai last week were brief and unproductive. U.S. Trade Representative Robert Lighthizer and Treasury Secretary Steven Mnuchin were in China for a little over 24 hours, and their itinerary consisted of a dinner the night they arrived and a meeting that lasted about three hours Wednesday.

Neither team was accompanied by large staffs needed for detailed technical discussions, as in past rounds. The talks last week involved fewer than 10 people, including interpreters.