Mr. Pompeo’s visit did not include a meeting with China’s leader, Xi Jinping, apparently another signal of displeasure by the Chinese. The secretary of state met with Mr. Xi during his last visit to Beijing, in June.

Last week, American officials said they were seeking meetings with the “leadership,” a phrase commonly used to refer to Mr. Xi. A notional schedule released during Mr. Pompeo’s trip listed a meeting with him.

But Chinese analysts said it would be highly unlikely for Mr. Xi to agree to see a cabinet-level American official, given the curdled relationship and Mr. Pence’s forthright speech. Instead of Mr. Xi delivering a tough message, Yang Jiechi, the state councilor, would do so, Chinese analysts said.

“Receiving Pompeo in Beijing by anyone is itself a ‘favor,’ considering what the Trump administration has done to China since early July,” said Shi Yinhong, professor of international relations at Renmin University in Beijing.

At a briefing at the Ministry of Foreign Affairs, its spokesman said the downturn in relations would not affect cooperation on North Korean issues. “In short, no,” Lu Kang, the spokesman said when asked if there would be a negative effect.

But cooperation on North Korea — one of the important issues on which the two sides have worked together — seemed increasingly unlikely. North Korea has not agreed to Washington’s major request for the first step toward denuclearization: an inventory of all its nuclear assets. The North’s adamance means this is an issue that China would not be able to assist with, analysts said.

And while Washington wants to keep the pressure on North Korea’s economy by enforcing strict United Nations sanctions, China now opposes that stance. At the United Nations last month, Mr. Wang, the foreign minister, proposed an easing of sanctions against the North, and China has begun to allow certain kinds of trade to flow across the countries’ shared border.