“We’re going to zero,” Mr. Pompeo said. “We’re going to zero across the board.”

The United States and China have been closing in on an agreement that would cover a wide range of trade issues.

Negotiations are expected to continue over the next two weeks, first in Beijing and then in Washington, to resolve several sticking points, including removing current tariffs. If those gaps are bridged, the two sides will look to schedule a signing meeting between Mr. Trump and President Xi Jinping of China in May or June, said a person who has been briefed on the talks and spoke on the condition of anonymity to discuss them.

Any move by Beijing to keep buying Iranian oil — which analysts predicted China almost certainly will find some way to do — would force the United States to decide whether to impose sanctions on Chinese financial institutions, which are increasingly important in the worldwide economy. China could also set up a new vehicle as an alternative to using the current banking mechanisms, as the European nations have done to keep doing some business with Iran.

“Iran sanctions are going to be a big challenge for the U.S.-Chinese relationship,” said Jason Bordoff, the director of Columbia University’s Center on Global Energy Policy and a former energy adviser to President Barack Obama.

He added that if Chinese imports do not drop quickly, the American sanctions could be applied to Beijing’s central bank, the People’s Bank of China.

The United States and China are already at odds over an incendiary case involving Iran sanctions.

In January, Canadian authorities arrested a top Chinese technology executive, Meng Wanzhou, at the Vancouver airport at the request of American officials. The Justice Department is seeking her extradition to face charges of helping her company, Huawei, evade sanctions on Iran in a scheme that involved tricking American banks.

That case has been criticized by Chinese officials, who have said it is motivated purely by politics. It also heightened fury and grievances from the Chinese government over sanctions imposed by the United States on Iran in the administrations of both Mr. Obama and Mr. Trump. Chinese companies have many business ties to Iran.