The Bolshoi Ballet, the storied company whose name is synonymous with ballet, is considering two tours of China this year. The State Hermitage Museum in St. Petersburg, an art institution, is working to open a sister branch in Serbia, after losing partnerships in the West because of the invasion. A St. Petersburg ballet company recently brought two works by the Russian choreographer Boris Eifman, “Anna Karenina” and “The Pygmalion Effect,” to Kazakhstan. Star Russian musicians who were once regulars in New York and Berlin, including the pianist Denis Matsuev, who was seen as close to Mr. Putin, are booking engagements instead in Dubai, Istanbul and Belgrade, Serbia, among other cities.

China, with its legions of concertgoers and skepticism of Western ideals, has emerged as an attractive market for Russian artists aligned with Mr. Putin. While the two countries have long had cultural ties — Mr. Gergiev has been visiting the country for decades — the timing of his visit, coming a week after the meeting between Mr. Putin and Mr. Xi, suggested Russia and China were eager for a fresh display of camaraderie as they work to counter American dominance.

“Russia is looking for cultural exchanges wherever it can get them, just as it is looking for allies in technology, energy and the military,” Simon Morrison, a specialist in Russian music at Princeton University, said. “Putin is desperate to show that Russia still has friends.”

Russia’s attempts to use culture to soften its image abroad face significant challenges, even in friendly countries, experts say, because of its continuing attacks on Ukraine.

Classical music, dance, theater and visual art were “some of the last bridges between Russia and the West,” said Vera Ageeva, an international relations scholar at Sciences Po in France. But the disappearance of these cultural exports presents a “huge, incalculable loss for Russia and its soft power,” she said, which cannot be offset simply by expanding cultural ties with allies.