“We will not start a war — however, if someone starts a war, we will definitely fight back,” Gao Feng, China’s commerce ministry spokesman, said at a news conference in Beijing on Friday, the same day that United States Treasury Secretary Steven Mnuchin acknowledged the “potential of a trade war” in an interview with CNBC.

In a Sunday morning appearance on the CBS show “Face the Nation,” Mr. Mnuchin did not comment on whether discussions with China had advanced.

“I don’t expect there will be a trade war. It could be, but I don’t expect it at all,” he said. “But the president is willing to make sure we have free and fair trade, as you’ve seen his tweet already this morning.”

The tariffs proposed by Mr. Trump seem designed to protect American consumers but could hurt businesses that depend on products and materials from China, while a trade war would threaten farmers who export their goods.

Mr. Trump has argued that the short-term risks of a trade war escalation are outweighed by the long-term benefits of a more balanced trade relationship with China.

The dueling tariff proposals began last month, when Mr. Trump announced a plan to tax steel and aluminum from China and other countries. Since then, he has threatened to impose tariffs on other products, such as electronics. China has made similar threats about American cars, wine, soybeans and other exports.