WASHINGTON — President Trump defended his pugnacious approach to trade policy on Friday and the Treasury secretary warned there could be a trade war with China, as Mr. Trump doubled down on a White House plan to punish Beijing by threatening to levy tariffs on an additional $100 billion in imports.

“There is the potential of a trade war,” Steven Mnuchin said in an interview with CNBC. “There is a level of risk that we could get into a trade war.”

Mr. Mnuchin said he was hopeful that negotiations with his Chinese counterparts could avert a damaging escalation of retaliatory, tit-for-tat tariffs but declined to elaborate on the status of talks and whether he thought an agreement could be reached.

Financial markets continued to drop on Friday as the potential for a damaging trade dispute — which had begun to fade on Wednesday and early Thursday as other top White House advisers tried to soothe markets — reared its head amid comments by Mr. Trump, Mr. Mnuchin and Robert Lighthizer, the United States trade representative, suggesting the United States would not back down.