An austere greeting on the airport tarmac in Beijing sans a red carpet. A stone-faced handshake from China’s top foreign policy official. A seat looking up at the Chinese leader, Xi Jinping, perched at the head of a long table.

To international audiences, the optics of Secretary of State Antony J. Blinken’s two-day visit to Beijing barely raised any eyebrows. Foreign ministers are rarely, if ever, met with much fanfare at the airport. And an audience with a head of state alone is a sign of great importance and respect.

But to nationalist-leaning audiences in China, especially on social media, the scenes tell a different story. To them, the Mr. Blinken arrived only after months of pleading for an invitation. And during his visit, he was schooled on respecting China’s interests and played supplicant to Mr. Xi. Chinese social media users gleefully noted that Mr. Blinken arrived on Father’s Day, the implication being — using the parlance of the internet — that Mr. Xi was America’s daddy.

The nationalistic commentary in China around Mr. Blinken’s visit underscored a point that Mr. Xi made in his meeting with the top American diplomat on Monday: “Major-country competition does not represent the trend of the times.” The translation: Surrounding China with security partners and cutting off its access to advanced technology is not healthy competition, but an invitation for conflict.

Mr. Xi’s rejection of the framing of U.S.-China relations by the two most recent American presidents raises doubts about whether the world’s two superpowers can reach a strategic accommodation with each other in the coming years.

“They apparently don’t buy into this framework at all,” said Bonnie Glaser, managing director of the Indo-Pacific program at the German Marshall Fund of the United States.

“That begs the question: Is it then possible to stabilize relations?”

It is unclear to what extent the state played a role in promoting the triumphant narrative online, though Chinese censors generally have broad controls to sway public opinion. Even in China’s more staid state-controlled news outlets, which mostly carried the government’s summaries of the meetings, coverage of the visit emphasized Beijing’s view that Mr. Blinken was visiting to reassure the Chinese government and listen to its concerns.

Casting China as a strong and responsible power willing to lower tensions with a belligerent United States may help mask the less politically palatable reasons Beijing wants to re-engage with Washington, analysts say. Chief among them is the need to stabilize the Chinese economy, which has been struggling to maintain a recovery after coming out of three years of punishing pandemic restrictions.

“The optics of Xi Jinping lecturing to a subordinate American secretary of state from the head of a boardroom table plays well to a domestic audience that China is a global power that not only demands, but receives, respect from other great powers,” said Drew Thompson, a visiting senior research fellow at the Lee Kuan Yew School of Public Policy in Singapore.

He noted that Mr. Blinken’s two immediate predecessors — Mike Pompeo and Rex W. Tillerson — were seated next to Mr. Xi in armchairs when they met. (Mr. Xi sat with Mr. Pompeo in Beijing in June 2018, but did not meet the U.S. secretary when he returned that October.) Others pointed out that Bill Gates was invited to sit down next to a smiling Mr. Xi in an ornate wooden chair last week.

American officials say Mr. Blinken’s trip was necessary because maintaining regular high-level diplomacy between the world’s two superpower rivals — and its two largest economies and militaries — is critical to avoiding open conflict. Not only do the two governments seek stability in the relationship, but so do their allies and other nations. And diplomacy allows the two sides to make their views clear in private and public talks.

“If you want to stand up for American values on human rights and if you want to free detained Americans here or enlist China’s help on the fentanyl crisis, you can’t do it from the sidelines,” R. Nicholas Burns, the U.S. ambassador in Beijing, said in an interview on Tuesday. “You need to talk to them and press them as Secretary Blinken did on his visit here. You don’t give anything away by talking.”

“The Chinese received the secretary with a great deal of dignity,” added Mr. Burns, who was in all of Mr. Blinken’s meetings. “President Xi Jinping was very courteous in the meeting.”

Chinese officials, keen to turn the focus to commerce as an anchor in U.S.-China relations, had pushed for Janet L. Yellen, the Treasury secretary, and Gina Raimondo, the commerce secretary, to visit first, but American officials insisted that Mr. Blinken had to precede them. Now those other two U.S. cabinet officials are expected to travel to Beijing this summer, as is John Kerry, the climate envoy.

Analysts say China hopes the talks can help bolster business confidence when many of the traditional levers of Chinese economic growth, such as real estate, are facing dramatic challenges.

Moreover, China wants to underscore to the Biden administration its opposition to trade restrictions that choke Chinese access to important technologies, such as advanced semiconductor chips.

“Xi’s main motivation in entertaining the Americans is because the Chinese economy is in a really bad state,” said Willy Lam, an analyst of Chinese politics who is a senior fellow at Jamestown Foundation, a research institute in Washington. “Exports are down noticeably, and more U.S. and Western firms are moving production bases away from China.”

In hosting Mr. Blinken, China also sought to lay the groundwork for Mr. Xi to visit the United States in November for the Asia-Pacific Economic Cooperation summit — a trip that could lead to a one-on-one meeting with President Biden, the kind of visit would help burnish Mr. Xi’s image as a global statesman.

Beijing may also be moved by a sense of urgency to press the Biden administration for more assurances that it won’t inflame pro-independence sentiment in Taiwan, especially ahead of presidential elections in both the United States and Taiwan next year. In both places, politicians have ramped up rhetoric critical of the Chinese Communist Party during campaign years because they think that helps win votes.

China has been furious over the Biden administration’s growing support for the democratic, self-governed island — including a new trade agreement, more weapons sales and increased exchanges between officials. The Blinken visit gave China an opportunity to signal that it has warned the United States not to provoke Beijing over what its leaders have called the “core of China’s core interests.”

While Mr. Blinken’s visit may have helped end the freeze in top-level bilateral diplomacy, it also highlighted the fact that important dialogue between the two nations remains imperiled by China’s attitude over Taiwan and the widening military and economic rivalry.

After House Speaker Nancy Pelosi visited Taiwan last August, Beijing froze formal interactions with Washington on military issues, climate change and narcotics. China has only agreed to restore talks on climate change. U.S. officials went into the meetings in Beijing hoping to get China to reopen direct channels of military-to-military communications, including ones between the U.S. defense secretary, the chairman of the Joint Chiefs of Staff and the head of the Indo-Pacific Command and their Chinese counterparts.

Chinese officials meeting with Mr. Blinken rejected the request.

Olivia Wang contributed reporting.