After three years of self-isolation by China, President Biden’s top aides are flying into Beijing throughout the summer to try to convince and cajole Chinese officials, including Xi Jinping, the nation’s leader, on building a new foundation for relations.

It could amount to the most consequential diplomatic push of Mr. Biden’s presidency. He is betting that high-level dialogue can itself act as a ballast in a relationship that has been in a dangerous free fall for years. “I think there is a way to resolve, to establish a working relationship with China that benefits them and us,” Mr. Biden said in a CNN interview broadcast on Sunday, as Treasury Secretary Janet L. Yellen was ending her visit to Beijing.

Ms. Yellen met for hours with China’s premier, Li Qiang, and with a vice premier and top economic aide to Mr. Xi who was relatively unknown to U.S. officials — a sign that these exchanges might help establish important one-on-one channels. Since May, the C.I.A. director and the secretary of state have also traveled to Beijing, and the special climate envoy and the commerce secretary are following soon.

Mr. Biden and his aides say forging these personal ties could be necessary for defusing crises between the world’s two main superpowers. But the recent visits have also thrown into sharp relief the worsening structural problems in the relationship, ones that some analysts say could lead to armed conflict if mismanaged.

The diplomacy has done nothing to address the single thorniest issue between the two nations — the status of Taiwan — and China’s military ambitions in the Asia-Pacific region, which are incompatible with U.S. military dominance there. When Secretary of State Antony J. Blinken met with Mr. Xi in June, the Chinese leader refused to even acknowledge there needed to be a framework for the rivalry.

That means China will continue to view a wide range of policies by Washington as hostile acts, including export controls on advanced semiconductor technology and new military agreements with other Asian nations. American and Chinese officials recognize the relationship is becoming increasingly defined by military tensions, with talk of a possible war being normalized in the two capitals.

For the first time, Mr. Xi said publicly this year that the United States was trying to enact “all-around containment” of China, and there is no indication yet that the diplomacy this summer is disabusing him of that notion.

Mr. Biden said in his interview that Mr. Xi called him as the United States was strengthening its military alliances in the region and asked, “Why are you doing that?” Mr. Biden said he replied: “We’re not doing that to surround you. We’re doing that to maintain stability in the Indian Ocean and in the South China Sea” and to reinforce norms over the use of international waters and airspace.

U.S. officials say that the two militaries are having increasingly risky naval and air contacts, and that any accident could precipitate a crisis. But military diplomacy remains a yawning gap in relations.

Mr. Xi and his aides rebuffed Mr. Blinken when he asked for them to reopen senior-level military-to-military channels, which China shut down after Speaker Nancy Pelosi visited Taiwan last August. And in early June, Defense Secretary Lloyd J. Austin III got the cold shoulder from his Chinese counterpart, Gen. Li Shangfu, at an annual security conference in Singapore. The U.S. government imposed sanctions on Mr. Li in 2018 over purchases of military equipment from Russia.

Both the Biden administration and Chinese officials are bracing for domestic U.S. politics to add to strains next year. Republican and Democratic candidates in the 2024 elections are expected to try to outperform one another in hawkish rhetoric on China. U.S. officials say the trips this summer are intended to give the two governments a chance to have frank conversations about the relationship before the political campaigning heats up.

“For the Chinese, this year is the last chance before things presumably turn much more sour next year with the U.S. presidential election,” said Yun Sun, a scholar of China’s foreign policy at the Stimson Center in Washington. “Combined with China’s own economic challenges, especially the sluggish recovery, Beijing has incentives to make amends. Washington does, as well.”

China wanted to receive U.S. economic cabinet officials ahead of Mr. Blinken, but the Biden administration insisted that Mr. Blinken had to be the first official to visit after the secret trip of William J. Burns, the C.I.A. director, in May.

Chinese officials avoided making commitments with Mr. Blinken on any major issues, including on limiting exports of precursor chemicals used to make fentanyl, for which China is the main supplier. Chinese officials are suspicious of Mr. Blinken, who regularly raises issues of strategic competition and human rights. In February, he canceled his initial plans for a visit because of a Chinese spy balloon episode, and he said publicly that same month that China was considering sending military aid to Russia for use in Ukraine.

Ms. Yellen got a warmer reception starting last Thursday. China’s finance ministry issued a lengthy statement on Monday describing her comments in favorable terms seldom seen in other recent declarations on U.S.-China relations. The statement highlighted Ms. Yellen’s insistence that the United States is not seeking to decouple, or unplug, its economy from China’s. Less than two weeks ago, China’s premier warned in a speech that the United States was trying to do just that.

Perhaps most important, the finance ministry’s statement echoed recent calls by Ms. Yellen and Mr. Blinken for the United States and China to collaborate in areas where they have common interests, including global economic stability and climate change. “Effectively addressing global challenges requires coordination and cooperation between China and the United States,” it said.

R. Nicholas Burns, the U.S. ambassador in Beijing, said in an interview that “direct engagement at the cabinet level with the Chinese leadership is very much in the U.S. interest.”

“In the wake of visits by Secretaries Blinken and Yellen, we are in a stronger position to raise face to face the many areas of disagreement between our governments,” he added, as well as push China on the fentanyl issue and try to make progress on areas of cooperation: climate change, global health, food security and agriculture.

A senior Treasury Department official said on Ms. Yellen’s flight back to Washington that her trip was successful in establishing ties with China’s new economic team and “setting a floor in the relationship” between the United States and China — a favorite phrase among U.S. officials to describe efforts with China.

The official, who spoke on the condition of anonymity to frankly discuss diplomatic talks, said that Ms. Yellen and her team gained a better understanding of how China’s economic policy team is structured and how it sees the health of the Chinese economy. The official said the Treasury hopes communication at multiple levels will happen more often to avoid misunderstandings. But the official declined to say whether Ms. Yellen had invited He Lifeng, the Chinese vice premier and economist who is close to Mr. Xi, to Washington.

Eswar Prasad, a Cornell University professor who studies China’s economy, said Ms. Yellen’s “willingness to engage with China’s economic leadership on a range of substantive issues while acknowledging differences and explaining the rationale for U.S. actions will set the tone for more constructive discussions.”

“While any significant de-escalation of mutual economic hostilities is not in the cards, Yellen’s visit might help limit any further escalation in bilateral economic and trade tensions despite rising anti-China rhetoric in Washington,” he said.

However, the two governments expect more clashes on investment limitations, export controls and sanctions. American officials have tried to signal to Chinese officials that this is a new normal in relations — that the United States plans to cut off very specific trade links with China because of national security concerns. The idea was most clearly expressed by Jake Sullivan, the national security adviser, in an April speech when he said the United States would protect “foundational technologies with a small yard and high fence.”

The Chinese government continues to push back against American sanctions on hundreds of Chinese entities and individuals that have been imposed as punishment for human rights abuses in Xinjiang, Tibet and Hong Kong.

Some Chinese scholars are skeptical that the good will from Ms. Yellen’s visit will last. Shi Yinhong, an international relations professor at Renmin University in Beijing, said that Ms. Yellen’s most important comments were those in which she said the United States would continue diversifying supply chains away from China and would take targeted actions to defend its national security.

“It summarizes two fundamental policies the U.S. has taken persistently and with repeated escalations,” he wrote in a text message.

Wu Xinbo, the dean of international studies at Fudan University, said the long-term effect of Ms. Yellen’s visit “depends on how this will translate into policy.” Technology issues have moved so much to the center of the relationship that Commerce Secretary Gina Raimondo’s visit will be critical in showing whether the United States is ready to address China’s concerns, he said.

“To some extent, her visit is more important than Yellen’s visit,” he said.

China has agreed to resume climate dialogue after suspending it last August. John Kerry, the special climate envoy, plans to land in Beijing on Sunday for four days of talks. China and the United States are the two largest emitters of greenhouse gases, and China’s coal use keeps growing despite its parallel expansion of renewable energy capacity.

“There’s a lot of heavy lifting that now needs to be done to achieve our goals,” Mr. Kerry said in an interview last Thursday, “and the news coming out of the scientific community around the world should be highly alarming to everybody.”

At least three Chinese ministers are expected to visit the United States by October. That would pave the way for what is likely to be the most important diplomatic engagement of the year: Mr. Biden and Mr. Xi meeting in San Francisco in November on the sidelines of an economic summit of Asia-Pacific nations.

Lisa Friedman contributed reporting.