Beijing — U.S. Secretary of State Antony Blinken met Monday with Chinese President Xi Jinping as he wrapped up a two-day, high-stakes visit to Beijing aimed at easing soaring tension between the countries. The meeting at the Great Hall of the People had been expected and was seen as key to the success of the trip, but neither side confirmed it would happen until a State Department official announced it just an hour beforehand.

Speaking to reporters at the U.S. Embassy in Beijing after his meeting with China's leader, Blinken said he had stressed during his two days of sit-downs with senior Chinese officials "that direct engagement and sustained communication at senior levels is the best way to responsibly manage differences and ensure that competition does not veer into conflict." 

"I heard the same from my Chinese counterparts," Blinken said. "We both agree on the need to stabilize our relationship."

Blinken insisted the U.S. government's goal was not, as Beijing has often suggested, the "economic containment" of China, but he said Washington had "no illusions about the challenges of managing this relationship," acknowledging that there were "many issues on which we profoundly — even vehemently — disagree."  

In earlier meetings between Blinken and senior Chinese officials, the two sides expressed willingness to talk but showed little inclination to bend from hardened positions on disagreements ranging from trade, to Taiwan, to human rights conditions in China and Hong Kong, to Chinese military assertiveness in the South China Sea, to Russia's war in Ukraine.

Blinken called his two days of talks with senior Chinese officials "candid and constructive," but said diplomatic efforts would have to continue on multiple fronts, and acknowledged that "progress is hard." 

"My hope and expectation is we will have better communications, better engagement going forward," said the top U.S. diplomat.  

In one notable diplomatic shortcoming, Blinken said China did "not agree to move forward" with re-establishing direct military-to-military communications, calling it a "continuing priority" for the Biden administration, and one that "we have to keep working on."   

In video of their meeting released by Chinese state broadcaster CCTV, Xi could be heard saying: "The two sides have agreed to follow through on the common understandings President Biden and I have reached in Bali."

Xi said that the two sides had made progress and reached agreements on "some specific issues" without elaborating. "This is very good," Xi said.

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"I hope that through this visit, Mr. Secretary, you will make more positive contributions to stabilizing China-U.S. relation," Xi added.

Standing beside the Chinese leader, Blinken said President Biden had sent him to Beijing "because he believes that the United States and China have an obligation and responsibility to manage our relationship. The United States is committed to doing that.  It's in the interest of the United States, in the interests of China, and in the interest of the world." 

Despite Blinken's presence in China, he and other U.S. officials had played down the prospects for any significant breakthroughs on the most vexing issues facing the planet's two largest economies. Instead, these officials have emphasized the importance of the two countries establishing and maintaining better lines of communication.

Blinken is the highest-level American official to visit China since Mr. Biden took office and his two-day trip comes after his initial plans to travel to China were postponed in February after the shootdown of a Chinese surveillance balloon over the U.S. His visit was expected to usher in a new round of visits by senior U.S. and Chinese officials, possibly including a meeting between Xi and Mr. Biden in the coming months.

Blinken met earlier with China's top diplomat, Wang Yi, for about three hours, according to a U.S. official. Wang told Blinken that "China has no room to compromise or concede" on Taiwan.

"The United States must... respect China's sovereignty and territorial integrity and clearly oppose 'Taiwan independence,'" the statement added. 

Blinken, speaking after his meetings, stressed the U.S. commitment to the status quo with Taiwan, reiterating Washington's official stance that the U.S. does not support independence for Taiwan.

"At the same time," Blinken added, "we and many others have deep concerns about some of the provocative actions that China has taken in recent years going back to 2016."

China's Ministry of Foreign Affairs wrote in a statement that Blinken's trip to Beijing "coincides with a critical juncture in China-U.S. relations, and it is necessary to make a choice between dialogue or confrontation, cooperation or conflict," and blamed the "U.S. side's erroneous perception of China, leading to incorrect policies towards China" for the current "low point" in relations.

It said the U.S. had a responsibility to halt "the spiraling decline of China-U.S. relations to push it back to a healthy and stable track."

Despite Blinken's presence in China, he and other U.S. officials had played down the prospects for any significant breakthroughs on the most vexing issues facing the planet's two largest economies.

Instead, they have emphasized the importance of the two countries establishing and maintaining better lines of communication.

The State Department said Blinken, in his meeting with Wang, "underscored the importance of responsibly managing the competition between the United States and the PRC through open channels of communication to ensure competition does not veer into conflict."

In the first round of talks on Sunday, Blinken met for nearly six hours with Chinese Foreign Minister Qin Gang, after which both countries said they had agreed to continue high-level discussions. 

One official in the room told CBS News' Margaret Brennan both sides agreed that they want to stop the downward spiral in the relationship but it is clear there are still profound differences.

Senior State Department officials told reporters the meeting lasted five and a half hours and was followed by a two-hour dinner. Both sides were "very direct and very candid" and both expressed a desire to "stabilize the relationship," the officials said.

The two sides both said Qin had accepted an invitation from Blinken to visit Washington but Beijing made clear that "the China-U.S. relationship is at the lowest point since its establishment." That sentiment is widely shared by U.S. officials.

Mr. Biden and Xi had made commitments in Bali last year to improve communications "precisely so that we can make sure we are communicating as clearly as possible to avoid possible misunderstandings and miscommunications," Blinken said before leaving for Beijing.

In his meetings on Sunday, Blinken also pressed the Chinese to release detained American citizens and take steps to curb the production and export of fentanyl precursors that are fueling the opioid crisis in the United States.

Xi offered a hint of a possible willingness to reduce tensions Friday, saying in a meeting with Microsoft Corp. co-founder Bill Gates that the United States and China can cooperate to "benefit our two countries."

Since the cancellation of Blinken's trip in February, there have been some high-level engagements. CIA chief William Burns traveled to China in May, while China's commerce minister traveled to the U.S. And Mr. Biden's national security adviser Jake Sullivan met with senior Chinese foreign policy adviser Wang Yi in Vienna in May.

But those have been punctuated by bursts of angry rhetoric from both sides over the Taiwan Strait, their broader intentions in the Indo-Pacific, China's refusal to condemn Russia for its war against Ukraine, and U.S. allegations from Washington that Beijing is attempting to boost its worldwide surveillance capabilities, including in Cuba.

Earlier this month, China's defense minister rebuffed a request from U.S. Defense Secretary Lloyd Austin for a meeting on the sidelines of a security symposium in Singapore, a sign of continuing discontent.

Meanwhile, the national security advisers of the United States, Japan and the Philippines held their first joint talks last week and agreed to strengthen their defense cooperation, in part to counter China's growing influence and ambitions.

This coincides with the Biden administration inking an agreement with Australia and Britain to provide the first with nuclear-powered submarines, with China moving rapidly to expand its diplomatic presence, especially in the Indian Ocean and the Pacific island nations, where it has opened or has plans to open at least five new embassies over the next year.

The agreement is part of an 18-month-old nuclear partnership given the acronym AUKUS — for Australia, the United Kingdom and the United States.

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