President Biden and his allies spent much of the G7 summit in Hiroshima, Japan, announcing new arms packages for Ukraine, including a pathway to providing F-16 fighter planes. They spent hours discussing strategy with President Volodymyr Zelensky for the next phase of a hot war started by Russia.

So it was easy to miss Mr. Biden’s prediction on Sunday of a coming “thaw” in relations with Beijing, as both sides move beyond what he called the “silly” Chinese act of sending a giant surveillance balloon over the United States, only the most recent in a series of incidents that have fueled what seems like a descent toward confrontation.

It is far too early to say whether the president’s optimism is based on the quiet signals he has received in behind-the-scenes meetings with the Chinese government in recent weeks.

Mr. Biden’s own aides see a struggle underway in China between factions that want to restart the economic relationship with the United States and a far more powerful group that aligns with President Xi Jinping’s emphasis on national security over economic growth. As this weekend showed, China is enormously sensitive to any suggestion that the West is organizing a challenge to Beijing’s growing influence and power.

So if Mr. Biden is right, it may take a while for the ice to melt.

Facing a new, unified set of principles from the major Western allies and Japan on how to protect their supply chains and their key technology from Beijing — contained in the meeting’s final communiqué — China erupted in outrage.

Beijing denounced what it portrayed as a cabal seeking to isolate and weaken Chinese power. The Japanese ambassador to Beijing was called in for a reaming out, and China moved to ban products from Micron Technology, an American chip maker, on the grounds that its products posed a security risk to the Chinese public. It seemed like exactly the kind of “economic coercion” the world leaders had just vowed to resist.

Mr. Biden often says he has no desire to see a new cold war begin with China. And he points out that the economic interdependencies between Beijing and the West are so complex that the dynamic between the two countries is entirely different from what it was when he was delving into foreign policy for the first time as a newly elected senator, 50 years ago.

The harmony in Hiroshima over developing a common approach, and the blasts from Beijing that followed, suggested that Mr. Biden had made progress on one of his top foreign policy priorities despite underlying tension among the allies. Rather than dwell on their disagreements, the leaders of the major industrial democracies lined up their approach to China in a way that Beijing clearly saw as potentially threatening, some analysts noted after the meeting.

“One indication that Washington would be pleased is that Beijing is so displeased,” said Michael Fullilove, the executive director of the Lowy Institute, a research group in Sydney, Australia.

Matthew Pottinger, a former deputy national security adviser to President Donald J. Trump, and the architect of that administration’s approach to China, agreed. “The fact Beijing was so touchy about the G7 statements is an indicator the allies are moving in the right direction.”

Mr. Biden and the other leaders of the G7 — which includes Britain, Canada, France, Germany, Italy and Japan — wrote their first joint statement of principles about how they would resist economic blackmail and dissuade China from threatening or invading Taiwan, while seeking to reassure Beijing that they were not seeking confrontation.

The communiqué pressed China on the usual stress points, including its military buildup in the South China Sea and the widely documented human rights abuses against Uygurs and other Muslims in Xinjiang. Four months after the United States quietly began distributing intelligence to the European allies suggesting that China was considering sending arms to Russia to fuel its fight in Ukraine, the document seemed to be a warning to Beijing against pressing its “no limits” relationship with Russia too far.

Yet the democracies also left the door open to improving relations with Beijing by making clear that they were not attempting a strategy of Cold War containment against the world’s ascendant economy, even as they seek to cut China off from key technologies — including the European-made machinery critical to producing the most advanced semiconductors in the world.

“Our policy approaches are not designed to harm China nor do we seek to thwart China’s economic progress and development,” the communiqué said. “A growing China that plays by international rules would be of global interest. We are not decoupling or turning inwards. At the same time, we recognize that economic resilience requires de-risking and diversifying.”

“De-risking” is the new term of art, created by the Europeans, to describe a strategy of reducing their dependence on Chinese supply chains without “decoupling,” a far more severe separation of economic relations. Mr. Biden’s team has embraced the phrase, and the strategy — meant to sound self-protective rather than punitive — has become a staple of the recent conversation about how to deal with Beijing. Jake Sullivan, the national security adviser, talks of “building a high fence around a small yard” to describe the protection of key technologies that could bolster China’s rapid military buildup.

But what looks like risk reduction to the United States and Europe can look like a nicely worded containment strategy in Beijing.

The consensus reached in Hiroshima came after what Michael J. Green, a former top Asia adviser to President George W. Bush, called “a string of diplomatic wins for the U.S. and losses for China.” He has worked behind the scenes to promote a rapprochement between South Korea and Japan, and is planning to integrate Japan into a consultative group on nuclear strategy and deterrence that it announced during a state visit last month by Yoon Suk Yeol. If successful, it would create a far tighter nuclear alliance in China’s neighborhood.

“From Beijing’s perspective, this has been a week of even closer alignment among the other powers in the region with the United States,” said Mr. Green, now the chief executive of the United States Studies Center at the University of Sydney.

China pushed back hard. In a statement issued over the weekend, it accused the G7 of “obstructing international peace,” “vilifying and attacking China” and “crudely meddling in China’s domestic affairs.” The same day it accused Micron of “relatively serious cybersecurity problems” that could threaten national security, the same argument the U.S. makes about TikTok and Huawei.

Despite the common ground in Hiroshima, Mr. Biden’s decision to cancel the second half of his trip to the Pacific, including a stop in Papua New Guinea, so he could rush home to deal with domestic spending and debt negotiations, was taken as a setback in the competition with China.

Now the question is whether, quietly, Mr. Biden can rebuild a relationship with Mr. Xi that seemed to be turning around last fall, after their first face-to-face meeting.

Mr. Biden referred to the spy balloon incident in interesting ways on Sunday.

“And then this silly balloon that was carrying two freight cars’ worth of spying equipment was flying over the United States, and it got shot down, and everything changed in terms of talking to one another,” he said. “I think you’re going to see that begin to thaw very shortly.

If there is a turnaround, it may result from the quiet talks that Mr. Sullivan held in Vienna this month with Wang Yi, China’s top foreign policy official.

The sessions were hardly warm, but in some ways they were more candid and useful than American officials had expected. Rather than simply a recitation of talking points, as is typical of encounters with Chinese counterparts, Mr. Wang spoke in more unscripted terms than usual, according to officials familiar with the talks. There was an airing of grievances on both sides that the Biden team hoped would help clear the air.

There were long conversations in particular about Ukraine and Taiwan. Mr. Wang emphasized that China was not seeking conflict with Taiwan, apparently trying to assuage American officials who last summer feared that China might accelerate its plans to resolve its dispute over Taiwan by force.

Mr. Wang raised the need to avoid precipitous actions surrounding elections in Taiwan early next year. Mr. Sullivan pressed the point that China’s own conduct was raising the temperature and increasing risk of escalation.

Administration officials hope to return to a more regular dialogue with China, perhaps sending Treasury Secretary Janet L. Yellen and Commerce Secretary Gina Raimondo to China, and eventually rescheduling a trip to Beijing by Secretary of State Antony J. Blinken, who canceled a visit after the spy balloon episode. There is talk of a meeting between Mr. Biden and Mr. Xi in the fall.

But the war in Ukraine will continue to shadow the relationship — and so will the course of the relationship between Moscow and Beijing, what one of Mr. Biden’s aides calls “the alliance of the aggrieved.” Yet for the moment, U.S. officials have taken solace that China has not, so far as they know, provided lethal weapons to Russia despite President Vladimir V. Putin’s need for armaments.

David Pierson contributed reporting.