The leaders represented the three biggest powers bidding to reshape a global order dominated by the United States, convening over video feeds at a virtual summit meeting on Tuesday. But beyond the unity implied by their joint appearance, each seemed focused on his own, different aim.
For President Vladimir V. Putin of Russia, that meant projecting strength in the aftermath of the uprising by the Wagner mercenary group and claiming international support for his war in Ukraine.
For China’s top leader, Xi Jinping, the summit was another opportunity to assail the United States by calling for an end to “hegemonism” and “power politics.”
And for India’s prime minister, Narendra Modi, the meeting’s host, it was a way to signal his country’s rising stature — and to land a thinly veiled jab at its archrival, Pakistan, by calling for other nations to unite in a “fight against terrorism.”
The annual meeting of the Shanghai Cooperation Organization offered no dramatic statement of changing alliances in the leaders’ prepared remarks. But the forum — which was established by China and Russia in 2001 and includes Pakistan and the Central Asian countries Kazakhstan, Kyrgyzstan, Tajikistan and Uzbekistan — did provide a glimpse of how a regional club formed to counter Western influence might navigate their competing priorities.
There was no mention of the mounting friction between Beijing and New Delhi, which has driven the historically nonaligned India closer to the United States.
And if Mr. Putin had hoped that his fellow leaders might issue resounding statements of support to ease his weakened position at home and to defend his war in Ukraine, he had to settle for general optics and warm tones instead.
More important, with the Biden administration and much of the rest of the world watching, the forum fundamentally seemed to be a statement that the three leaders were in control of their domestic issues and prepared to usher in what Mr. Putin called a new “multipolar” world.
“They all have incentives to play things down and make it all look normal,” said Ian Chong, an associate professor of political science at the National University of Singapore. “They showed that things were under control and there aren’t any rifts despite Russia’s problems and India’s desire to explore ties with the U.S.”
No leader on Tuesday had a greater need to recast his image than Mr. Putin, who faced the biggest challenge to his more than two-decade rule last month when Wagner mercenary forces tried to topple Russia’s military leadership.
While Mr. Putin was able to defuse the crisis by agreeing to allow mercenary leader, Yegveny V. Prigozhin, to leave for Belarus, the brief insurrection raised questions about his authority and future.
Speaking at his first international forum since the mutiny, Mr. Putin thanked the member states for their backing after the uprising, which he claimed had no popular support in Russia.
“United by the deep responsibility for the fate of the motherland, Russian political circles and all of society showed a united front against the attempted armed mutiny,” Mr. Putin said. He also sought to cast the summit as a sign of international support for his invasion of Ukraine.
Nowhere is that support more important than from China, the only major nation to provide Russia with diplomatic and economic cover. China has done so because it has made a long-term bet on Mr. Putin as a necessary partner to challenge the United States.
That bet has come at a price, however, with Beijing struggling to mend ties with key economic partners in Europe. China’s refusal to condemn the war in Ukraine has also drawn more global attention to Beijing’s aggressive stance on Taiwan.
The virtual meeting provided Mr. Xi a chance to advance China’s goal of wresting influence from the United States. He touted the Shanghai Cooperation Organization as a way to “improve global governance” and promote “Chinese-style modernization” — coded language that expresses a vision of the world in which Beijing and its partners have a greater say in international rules and norms.
Where India fits in that vision remains to be seen. China’s largest emerging strategic rival, which joined the Shanghai Cooperation Organization in 2017, views the forum as a way to balance its ties with Western nations and its relationships with China and Russia.
India has maintained stable ties with Russia, mostly economic, after refusing to condemn the invasion of Ukraine. But its relations with China have worsened over border disputes and India’s membership in a security-focused coalition with the United States called the Quad. Beijing views the Quad as a tool to contain China.
A high-profile visit to Washington last month by Mr. Modi has intensified Chinese suspicions that India is drawing closer to the United States to blunt China’s rise.
Despite those tensions, India has a vested interest in the forum. It relies on Central Asian countries for energy supplies and to maintain influence in Afghanistan, which has a spillover effect on Pakistan.
Mr. Modi lauded the forum as “an important platform” for peace and prosperity, but urged the group to condemn countries that “use terrorism as an instrument of their policy.” The remark was a reference to Pakistan, which India accuses of sponsoring militants in the disputed Kashmir region.
“India will not abandon or quit the Shanghai Cooperation Organization as that would deprive it of a foothold in Central Asia and concede the Eurasian region to India’s main adversary, China,” said Sreeram Chaulia, dean of the school of international affairs at O.P. Jindal Global University near New Delhi.