NEW DELHI — When the top diplomats of four major Asia-Pacific nations met here in the Indian capital on Friday to discuss issues in the region, one had a direct message for the behemoth whose shadow loomed over the talk.

China must “act under the international institutions, standards and laws” to avoid conflict, Yoshimasa Hayashi, the foreign minister of Japan, said on a public panel that included his counterparts from the United States, India and Australia.

That request is one that every official on that stage has made on many occasions. Although Russia’s war in Ukraine has dominated diplomatic dialogue around the globe this past year, the dilemma of dealing with an increasingly assertive China is ever-present — and for many nations, a thornier problem than relations with Moscow. They subscribe to the framing that President Biden and his aides have presented: China is the greatest long-term challenge, and the one nation with the power and resources to reshape the American-led order to its advantage.

For President Biden and his aides, that tension came into sharp focus in recent weeks after a Chinese spy balloon began drifting over the continental United States, and when, in their telling, they came across intelligence that China is considering sending weapons to Russia for its war. That prospect has prompted American diplomats and those from allies and partners to deliver warnings to Chinese counterparts, including here in New Delhi.

The anxieties over both China’s and Russia’s increasingly discordant roles on the world stage were perhaps wrapped into a lament on Thursday by Prime Minister Narendra Modi of India that “multilateralism is in crisis today.”

“Global governance has failed in both its mandates” of preventing wars and fostering international cooperation, he said in a video address to a conference of top diplomats from the Group of 20 nations, made up of the world’s major economies, including China and Russia.

The four Asia-Pacific countries represented on the panel one day later at the Raisina Dialogue form the Quad partnership, which was revived in 2017 after many years of dormancy and has gained momentum since, mainly because of shared strategic concerns over China. But in a sign of the delicate balance they are trying to strike in relations with Beijing, the diplomats took pains to stress in their public comments that the Quad is not a security or military organization. Mr. Hayashi was the sole panelist to mention China, and only after being prompted by the panel’s moderator.

Their joint statement, released after private meetings, did not mention China, although many points in it, including the issue of “peace and security in the maritime domain,” are obviously aimed at Chinese policies.

At the earlier Group of 20 conference, the foreign minister of China, Qin Gang, joined the foreign minister of Russia, Sergey V. Lavrov, in playing the role of spoiler.

Together, they opposed two paragraphs in a proposed consensus communiqué, the first of which directly criticized Russia’s war in Ukraine. Even though the leaders of the Group of 20 had approved the same two paragraphs in a consensus document at a meeting last year in Bali, Indonesia, China has dug in with Russia to sabotage both this week’s communiqué and a similar one proposed at a G20 finance ministers’ conference in late February in Bengaluru, India.

The second paragraph in the communiqué that they objected to did not mention Russia or Ukraine. It simply said that all the nations agreed to uphold United Nations principles on international humanitarian law, “including the protection of civilians and infrastructure in armed conflicts” and forbidding “the use or threat of use of nuclear weapons.”

Some diplomats privately expressed surprise that China opposed a reiteration of such basic principles, a move that forced the conference to issue a lower-level chair’s statement. Mr. Qin’s stance seemed to validate concerns that his government was willing to side with Russia in a growing number of diplomatic venues — including at the United Nations Security Council — to undermine policies or actions that the vast majority of nations endorse.

“Russia and China were the only two countries that made clear that they would not sign on to that text,” Antony J. Blinken, the U.S. secretary of state, said pointedly at a news conference on Thursday night. He added that he agreed with Mr. Modi “that there are real challenges to the multilateral system.”

He noted, too, that at the U.N. Security Council, “we have two countries in particular that tend to block the attempted actions of the council to address some of the most urgent global concerns.”

Mr. Blinken has also expressed skepticism over a push by Beijing for peace negotiations in the war in Ukraine, saying Chinese officials are merely creating a smoke screen to buy Russia more time to press its assault.

Chinese officials say they will happily cooperate with countries in the international system, and that it is the United States fanning the flames of division with its “Cold War mentality.”

China is ready to work with other Group of 20 nations to both “stay committed to solidarity and cooperation” and “play a bigger role in addressing major global economic and financial challenges,” said Mao Ning, a Chinese Foreign Ministry spokeswoman, at a news conference in Beijing on Thursday as the meetings in New Delhi began.

After Mr. Blinken’s critical remarks, Ms. Mao said Friday that Mr. Qin had urged the Group of 20 nations to engage in “real multilateralism” and avoid “power politics and camps of confrontation.” She added that the G20 was an inappropriate venue for discussing Ukraine, and criticized the Quad partnership as a “closed small circle.”

Ms. Mao also lashed out at an announcement by the U.S. Commerce Department on Thursday that it was restricting trade with 28 Chinese entities that American officials accused of violating U.S. sanctions, including certain bans on nuclear and missile technology sales. That move, Ms. Mao said, showed the United States was going to great lengths to “suppress Chinese enterprises.”

The Biden administration has broadened an effort begun by the Trump administration to hobble Chinese companies that the U.S. government views as potential national security threats, including Huawei, China’s most important communications technology company. Last October, Mr. Biden announced sweeping restrictions on selling advanced semiconductors and semiconductor manufacturing equipment to China, in what aides called an effort to end China’s access to “foundational technologies.”

The Biden administration is pushing two allies, Japan and the Netherlands, to also impose further limits on sales of semiconductor manufacturing equipment to China. That subject might have come up when Mr. Blinken met in New Delhi with his Dutch and Japanese counterparts. The move is another manifestation of the Biden administration’s belief that China can be constrained only by getting allies and partners on the same page.

And Mr. Blinken warned China on Thursday night of economic penalties if it went ahead with giving weapons to Russia: “We have sanctions authorities of various kinds,” he said.

For world leaders, those irrepressible tensions are more evidence that the international system is cleaving into blocs, and that Mr. Modi’s urgent plea to diplomats this week was falling on deaf ears: “Focus not on what divides us, but on what unites us.”

Olivia Wang contributed research from Hong Kong.