It was a scene in eastern China almost certainly intended for an audience on the other side of the world: The leaders of China, Russia and India, the three largest powers not aligned with the West, smiling and laughing like good friends as they greeted each other at a summit on Monday.

It starts with Prime Minister Narendra Modi of India and President Vladimir V. Putin of Russia holding hands and walking into a meeting hall filled with other world leaders. They head straight for President Xi Jinping of China, shake hands and form a close circle. A few words are exchanged before translators join the huddle. Mr. Putin cracks a broad smile, and Mr. Modi lets out a big laugh. At one point, Mr. Modi joins hands with the other leaders.

The tableau carried multiple messages, analysts said. The bonhomie between Mr. Xi and Mr. Putin was meant to convey a close bond between them as leaders of an alternative world order challenging the United States. Mr. Modi sought to show that India has other important friends — including China, regardless of an unresolved border dispute — if the Trump administration chooses to continue alienating New Delhi with tariffs.

“Optics is a key part of this summit, and the White House should grasp that its policies will result in other countries looking for alternatives to meet their interests,” said Manoj Kewalramani, head of Indo-Pacific studies at the Takshashila Institution in Bangalore, India.

That imagery in the city of Tianjin, where more than 20 leaders from mostly Central Asia and South Asia gathered, showed how the geopolitical disruption caused by Mr. Trump has given China and Russia a platform to rally partners such as Iran, Kazakhstan, Kyrgyzstan, Belarus and Pakistan.