America and China may be back to having high-level government talks, but their battle for global power and influence remains unchecked. Mutual suspicion still runs deep.

U.S. Secretary of State Antony Blinken set low goals for his visit to Beijing in late June, and he met them. Seemingly the most the two rivals can hope for these days is to stop things from getting much worse.

Mr. Blinken pointed to difficult days ahead, while China’s foreign ministry warned the relationship was in a downward spiral.

“It was clear coming in that the relationship was at a point of instability, and both sides recognized the need to work to stabilize it,” Mr. Blinken said of the reason for his trip. “And specifically, we believe that it’s important to establish better lines of communication, open channels of communication, both to address misperceptions, miscalculations and to ensure that that competition doesn’t veer into conflict.”

Mr. Blinken’s two-day visit to the Chinese capital helped restore top-level ties, but China rebuffed a U.S. request to resume military-to-military contacts. Neither government appears convinced of the other’s honesty.

“Negative Assurances”

Speaking at a fundraiser for his 2024 reelection, President Joe Biden said Chinese President Xi Jinping had been “embarrassed” by the spy balloon Mr. Biden ordered shot down over U.S. airspace. This incident prompted Mr. Blinken to cancel an earlier trip to China.

“That’s what’s a great embarrassment for dictators, when they didn’t know what happened. That wasn’t supposed to be going where it was. It was blown off course up through Alaska and then down through the United States. And he didn’t know about it,” Mr. Biden said. “When it got shot down, he was very embarrassed. He denied it was even there.”

While the two countries say they are not enemies intent on harming each other, they are not pretending to be friends.

After the June meeting with Mr. Xi, Mr. Blinken acknowledged entrenched differences. “We have no illusions about the challenges of managing this relationship. There are many issues on which we profoundly, even vehemently, disagree,” he said.

Mr. Xi sounded a similar note but suggested that the rivalry could be overcome.

“The competition among major countries is not in line with the trend of the times and cannot solve the problems of the United States itself and the challenges facing the world,” he told Mr. Blinken. “China respects the interests of the United States and will not challenge or supplant the United States. Similarly, the United States should also respect China and not harm its legitimate rights and interests.”

Danny Russel, the top U.S. diplomat for Asia during the Obama administration who is currently vice president of the Asia Society Policy Institute in New York, said these so-called “negative assurances” that China respects the U.S. and is not looking to displace it—and that the U.S. is not trying to contain or hinder China—are important to prevent a collapse in ties.

“Both sides clearly used the visit to help stabilize the relationship, which has been lurching toward dangerously intense confrontation,” Mr. Russel said. And, although both the U.S. and China mentioned specific disagreements, especially about Taiwan, Mr. Russel said that “the public statements by the two sides were notably positive, particularly by recent standards.”

Yet Washington and Beijing remain deeply suspicious of each other’s actions and intentions.

Slow Progress

At a news conference concluding his trip to Beijing, the first by a U.S. secretary of state since 2018, Mr. Blinken said Washington had achieved its objectives for the trip, including raising concerns directly, trying to set up channels for dialogue and exploring areas of cooperation. But he said progress was not straightforward.

“The relationship was at a point of instability, and both sides recognized the need to work to stabilize it,” Mr. Blinken said before leaving China. “But progress is hard. It takes time. And it’s not the product of one visit, one trip, one conversation. My hope and expectation is: we will have better communications, better engagement going forward.”

U.S. officials had been playing down the prospect of a major breakthrough but hoped Mr. Blinken’s visit would pave the way for more bilateral meetings. This happened to be the case as Treasury Secretary Janet Yellen visited China in early July.

There is even talk of a summit between Mr. Xi and Mr. Biden later in the year.

The two leaders last met on the sidelines of the G20 summit in Indonesia in November, pledging more frequent communication, although ties have since deteriorated.

“The two sides have also made progress and reached the agreement on some specific issues. This is very good,” Mr. Xi told Mr. Blinken during their meeting.

Mr. Blinken responded by saying the two countries have a responsibility to manage their relationship.

His meetings in Beijing, including talks with China’s top diplomat Wang Yi and foreign minister Qin Gang, had been “candid and constructive,” Mr. Blinken added.

It was not clear from Mr. Xi’s remarks what progress he was referring to, although he told Mr. Blinken that China “hopes to see a sound and steady China-U.S. relationship” and believes that the countries “can overcome various difficulties,” according to a Chinese readout of the talks.

When Mr. Xi urged Washington not to “hurt China’s legitimate rights and interests,” this could signal potential flashpoints such as Taiwan, the democratic island Beijing claims as its own.

Mr. Blinken said he made clear that the United States needs much greater cooperation from China on stemming the flow of fentanyl, and the sides agreed to set up a working group on the matter.

Flashpoint Taiwan

The lack of open communication channels between the two countries has prompted international jitters, and Beijing’s reluctance to engage in regular military-to-military talks with Washington has alarmed China’s neighbors.

Speaking to reporters after the talks, senior foreign ministry official Yang Tao said U.S. sanctions were blocking progress on improving military-to-military communications.

Chinese defense minister Li Shangfu has been sanctioned since 2018 over the purchase of combat aircraft and equipment from Russia’s main arms exporter, Rosoboronexport.

Asked what specific progress the two sides had made, Mr. Yang said they had agreed to prevent a downward spiral in relations. The official added that Chinese foreign minister Qin had accepted Mr. Blinken’s request to visit the United States.

Mr. Xi’s comments, and the diplomatic choreography of the visit, appeared to signal a will to make progress, analysts said.

“China’s messaging has been pretty positive,” said Wu Xinbo, a professor and director at the Center for American Studies at Fudan University in Shanghai.

“China showed that it still hopes to work with the U.S. to stabilize and improve relations. I think that while China is not optimistic about Sino-U.S. relations, it has not given up hope either.”

Beijing’s tone on Taiwan was particularly pointed throughout Mr. Blinken’s visit.

“China has no room for compromise or concessions,” said Mr. Wang, according to the Chinese readout.

The United States has long stuck to a policy of “strategic ambiguity” over whether it would respond militarily to an attack on Taiwan, which Beijing has refused to rule out.

Uneasy Allies

United States Treasury Undersecretary Jay Shambaugh said that Washington would not hesitate to take targeted actions against China to secure the national security interests of the U.S. and its allies and to protect human rights. Such steely language is often heard from the leaders of both nations.

But, and there is almost always a but, Mr. Shambaugh also said the two countries must cooperate on global challenges.

While Beijing and Washington politically posture to demonstrate how committed they are to their positions, they also know they need one another to survive.

In prepared testimony before the U.S. Senate Foreign Relations Committee, Mr. Shambaugh said economic decoupling would be “disastrous” for both the U.S. and China and nearly impossible to achieve.

“When necessary, we will use a suite of tools to achieve our national security goals. It is our core mission to protect the American people from national security risks while also clearly communicating our position and intent to China to reduce the risk of misunderstanding,” said Mr. Shambaugh, who heads Treasury’s international affairs.

The Biden administration is weighing new restrictions on outbound private investment into China and other countries of concern. The Senate voted overwhelmingly in July to back legislation that would require U.S. companies to notify federal agencies of proposed investments in Chinese technologies such as semiconductors and artificial intelligence.

“To be clear: neither targeted national security actions nor attempts to build diversified supply chains represent decoupling,” Mr. Shambaugh said in the prepared remarks. “We seek a fair and healthy economic relationship that benefits both countries and supports American workers and businesses.”

Ms. Yellen’s visit to Beijing aimed to reopen communications and make the same points to China’s economic leaders, saying the trip put the relationship on “surer footing,” though the world’s two largest economies remained at odds over many issues.

Mr. Shambaugh said these differences included U.S. objections to Chinese “non-market” economic practices and excessive government support that put U.S. companies at a disadvantage. He added that the U.S. has also objected to China’s “economic coercion” to punish countries for diplomatic actions by cutting off imports or exports.

He also said that the Treasury had been troubled by China’s recent punitive actions against U.S. firms and export controls on critical minerals for semiconductors.

“While we are still assessing their impact, these actions reinforce the importance of our administration’s efforts to build resilient and diversified supply chains,” Mr. Shambaugh stated.

Can They Cooperate?

Mr. Shambaugh, who took over as the Treasury’s top economic diplomat in January, said the U.S. and China must also be able to cooperate on pressing global challenges, such as climate change and growing debt distress in developing countries. The Treasury’s engagement with China has yielded some dividends, including progress on debt restructurings for Zambia, Ghana and Sri Lanka, but more needs to be done, he added.

He also said protecting U.S. economic interests requires “strong and reliable international leadership.”

This includes stronger engagement with allies and partners, particularly low- and middle-income countries, he said, adding that this would also entail making sure that the International Monetary Fund and World Bank are “adequately” funded.

Ensuring that there is a sufficient amount of “high-standards” lending available to low-income countries through these and other international financial institutions will help keep them from becoming dependent on loans from China, he added.

Despite any small signs of change, widespread cooperation between the two nations appears far off.

Global Agendas

From the U.S. perspective, China’s rise has challenged its global position. Washington is racing to repair and shore up its relationships in regions where China has made inroads, particularly Africa and the Indo-Pacific, where America has opened or plans to open at least five new embassies this year.

Behind the scenes, the U.S. believes China has ulterior and perhaps nefarious motives.

An internal U.S. State Department document prepared earlier this year that focuses on China’s role at the United Nations and other international organizations said Beijing “believes that the People’s Republic of China must dominate and shape international institutions, standards and values in order to advance both its domestic and global agenda.”

“It views the established rules and norms in the U.N. system and other international organizations as privileging Westerns countries, supporting liberal democratic principles, and posing a threat to its monopoly on domestic political power and assertive global ambitions,” said the document, which is marked “SBU,” meaning “sensitive but unclassified” and was obtained by The Associated Press.

The document accuses China of having “undertaken a systematic campaign to subvert existing principles and standards, promote authoritarian ideology and policy [and] reprioritize economic development over human rights and democratic governance.”

In addition, it says China is working “to undermine or reshape international law and standards, institutions, and values to legitimize its own development and governance models, including related to human rights [and] using its economic and political influence to compromise institutions’ transparency, effectiveness, independence and alignment with foundational norms and values.”

From the Chinese perspective, the U.S. is clinging to fading glory as the world’s lone superpower and seeking to sabotage China’s development and growing international stature by sowing mistrust about Beijing’s intentions.

China’s top diplomat Wang Yi demanded that the U.S. stop “hyping the ‘China threat theory’” and “urged the United States not to project on China the template that a strong country must seek hegemony.”

He also said China should not be judged “in the vein of traditional Western powers,” concluding that a change of perspective “is the key on whether the U.S. policy towards China can truly return to objectivity and rationality.”

Discussions continue about a new meeting between Mr. Xi and Mr. Biden. At this point, however, it is not clear if China and the U.S. have found any issue of substance they can negotiate about. More talks could help with short-term easing of tensions but are unlikely to change the fact of a global rivalry.

This article contains information from The Associated Press.