A day after President Biden met with Chinese President Xi Jinping in Northern California in an effort to ease growing tensions between the two superpowers, Secretary of State Antony Blinken told CBS News that China represents "one of the most consequential relationships" the U.S. has with any nation.

"This is one of the most consequential relationships we have," Blinken told "CBS News Evening News" anchor and managing editor Norah O'Donnell Thursday. "One of the most consequential relationships between any two countries in the world. And we have an obligation to try to responsibly manage that relationship."

Among the most important results to come out of Wednesday's meeting near San Francisco was the two leaders agreeing that the U.S. and China would resume direct military-to-military communications.

"Yesterday, we agreed that our militaries would start talking again, at the most senior levels, and at the operational level," Blinken told CBS News. "And this is a very important way of trying to avoid a miscalculation, a mistake that could lead to a conflict."

Mr. Biden also said that Xi had agreed to cooperate with the U.S. on tackling the opioid crisis through counternarcotics efforts. In recent years, the U.S. has been working to halt the flow of precursor chemicals used to make fentanyl that are illegally trafficked to the U.S. from China.

"In terms of actually making a difference in the lives of the American people, the number one killer of Americans aged 18-to-49 is fentanyl," Blinken said. "Not car accidents, not guns, not cancer, it's fentanyl."

The chemical precursors, Blinken said, "have been coming from China, going to the Western Hemisphere, turned into fentanyl, and then coming into the U.S. We now have an agreement with China to take concrete action against the companies that are engaged in this practice."

A senior administration official told CBS News on Wednesday that the U.S. is working with the Chinese on a plan to have China use a number of procedures to go after specific companies that make those precursors. The official said the Chinese have already acted against several of the companies for which the U.S. has provided information. The official also said that China is taking a number of steps intended to curtail supplies used to make the chemicals.

"As the president said yesterday, 'trust but verify,' and that's what we're doing," Blinken said when asked if the U.S. can trust that China will follow through on the crackdown.

In his solo news conference following Wednesday's meeting, Mr. Biden for the second time this year referred to Xi as a "dictator" in response to a reporter's question.

"Well look, he is," Mr. Biden said. "I mean, he's a dictator in the sense that he is a guy who runs a country that is a communist country."

In June, Biden also called his Chinese counterpart a dictator while speaking to supporters during a private fundraising event in Northern California.

Cameras captured Blinken's uncomfortable response to Mr. Biden's remarks during Wednesday's news conference. A spokesperson for China's foreign ministry called the remarks "wrong" and "irresponsible."

When pressed by O'Donnell on whether Mr. Biden's comments were the position of the U.S. government, Blinken responded that the president "speaks for all of us."

"Well, it's not exactly a secret that we have two very different systems," Blinken said. "And the president always speaks candidly, and he speaks for all of us."

"It's clear that we will continue to say things and continue to do things that China doesn't like, just as I assume that they will continue to do and say things that we don't like," Blinken continued. "But what's so important about the meeting yesterday, about all the work we have been doing over the last six months to make sure that we're engaged diplomatically with them, is precisely to make sure, for the things that really matter: Pursuing this competition in a way that doesn't become conflict, managing our differences, and also looking for areas of cooperation."

— Kathryn Watson contributed to this report. 

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• Antony Blinken
• Fentanyl
• China