TOKYO — Even before President Biden traveled to Tokyo this week to strengthen a partnership with Australia, India and Japan, the alliance was struggling to present a united front, as India has refrained from joining the other nations in condemning Russia’s invasion of Ukraine.

Now, with remarks that President Biden made about Taiwan on Monday, the Indo-Pacific bloc is facing another, unexpected complication. On the eve of a summit of the four nations, Mr. Biden said he would defend the democratic island militarily if it were invaded by China, sending shock waves around the globe and placing the allies in a tricky position.

On Tuesday in Tokyo, Mr. Biden sought to temper his comments. Standing alongside the three other leaders of the grouping known as the Quad, he said his administration had not abandoned the “strategic ambiguity” over Taiwan long embraced by the United States. Asked if he would send in troops if China attacked Taiwan, Mr. Biden said, “The policy has not changed at all.”

Still, his comments the day before, when he answered “yes” after being asked by a reporter if he “was willing to get involved militarily to defend Taiwan,” left political leaders around the world trying to determine his true thinking and calibrate their own positions.

Mr. Biden’s remarks presented an immediate and probably unwanted challenge for Australia’s new prime minister, Anthony Albanese. Just hours after he was sworn in on Monday, Mr. Albanese flew to Tokyo with his new foreign minister, Penny Wong, who had harshly criticized her party’s election opponents during the campaign for suggesting that Australia would follow the United States into any war over Taiwan.

“Amping up the prospect of war against a superpower is the most dangerous election tactic in Australian history,” Ms. Wong said at the time.

Before the election, analysts had expected Mr. Albanese, if he became prime minister, to shift the government’s tone toward China, even if he did not make any major policy changes. Australia’s previous prime minister, Scott Morrison, often spoke about the Chinese government with belligerence as relations hit a decades-long nadir.

While Mr. Albanese was on his way to Tokyo, China’s premier, Li Keqiang, offered a message of congratulations, ending an almost three-year-long freeze in diplomacy between Australia and China with a call for “sound and stable” relations. Chinese state media said the meeting of the Quad, which it has called an anti-China alliance, would be viewed as an immediate test of Mr. Albanese’s “political wisdom.”

Now, raising questions once more about whether Australia would support a military defense of Taiwan could throw off whatever détente might be emerging. It also might shift the focus from subjects Mr. Albanese’s government would rather emphasize: greater ambition on climate change and increased aid and diplomatic engagement with countries in Southeast Asia and the Pacific islands.

Mr. Albanese and his administration would prefer “cautious, incremental change” on China, said James Curran, a historian at the University of Sydney. At the same time, he added: “They will not want to be seen easing up the pressure in terms of our policy on China.”

Japan, too, was put in a complicated position. With Japan’s westernmost inhabited island just 65 miles from Taiwan, a war with China could pull a nation that has disavowed armed conflict into dangerous territory.

The Japanese government is moving toward a large increase in defense spending as it confronts China’s growing ambitions in the region, and it has discussed plans to acquire weapons capable of striking missile launch sites in enemy territory.

But in contrast to Mr. Biden’s declaration on Monday, Prime Minister Fumio Kishida of Japan made an effort to maintain ambiguity when asked about Taiwan. “Our two countries’ basic position on Taiwan remains unchanged,” Mr. Kishida said.

While some hawks in Mr. Kishida’s governing Liberal Democratic Party said they were pleased that Mr. Biden had revealed his “true intentions,” more cautious voices expressed concern that the president could heighten tensions with China and accelerate an arms race.

Still, as the Quad leaders met on Tuesday, they sought to play up consensus where they could. The bloc announced new initiatives on cybersecurity, space, vaccine distribution and a data-sharing partnership to monitor shipping routes in the South China Sea, an effort to combat what the administration has described as aggressive maritime tactics by China in the region.

The nations released a joint statement calling for “peace and stability” in Ukraine and acknowledged “the tragic humanitarian crisis” the war had created. At the start of his meeting with Mr. Modi of India, Mr. Biden said the two of them would discuss the “unjustified invasion of Ukraine.” But Mr. Modi did not mention Russia.

His nation has been hesitant to criticize the Kremlin, in part out of fear of undermining its security and economic ties. Biden administration officials said that while the two nations disagreed on Russia, they could still collaborate on investments in the Indo-Pacific region that counter China’s growing influence.

Mr. Kishida, in a news conference after his own meeting with Mr. Modi, stressed that the two countries agreed on principles like the rule of law and sovereignty.

“No one should mistake the Quad for a partnership based on shared values, despite rhetoric along those lines,” said Aaron Connelly, a research fellow at the International Institute for Strategic Studies in Singapore. “The real hope among the four governments is that it develops into a balancing coalition which deters Beijing from aggressive actions along China’s periphery. This a coalition based on realpolitik, not values.”

Mr. Connelly, however, noted that “there is a lot of skepticism toward the Quad in Southeast Asia,” where nations are feeling unwanted pressure to choose sides between the United States and China.

“Many here see it as heightening geopolitical tensions in ways that raise risks,” Mr. Connelly said.

Mr. Biden’s remarks on Taiwan came as the United States launched a new economic framework with a dozen other allies meant to counter China’s dominance. Wang Yi, China’s foreign minister, said on Monday that the Indo-Pacific Economic Framework should not become a tool for America to “coerce regional countries to choose sides,” and he said attempts to box China in were bound to fail.

While China’s initial response on Monday to the president’s comments was relatively muted, Wang Wenbin, a spokesman for the foreign ministry, escalated his language on Tuesday, accusing the United States of implicitly supporting Taiwanese independence, a red line that Beijing has said it will never allow to be crossed.

“If it continues down the wrong path, this will not only cause irreversible damage to U.S.-China relations, but will also in the end make America pay an unbearable price,” Mr. Wang said. He quoted an old Chinese song: “When a friend comes, there is good wine; if a jackal comes, he will be greeted with a shotgun.”

Rahm Emanuel, the U.S. ambassador to Japan, said China’s words reflected its isolation.

“China wants America out of their backyard,” he said. “They hate that we have allies and friends, since it highlights all that they have is subjects and dependents. Everything we do in defense, national security, economic partnership and political engagement underscores our alliances and staying power.”

Reporting was contributed by Vivian Wang in Hong Kong, John Liu in Taipei, Damien Cave in Sydney, Australia, and Motoko Rich in Tokyo.

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