With Russia mired in a long war in Ukraine and increasingly dependent on China for supplies, Beijing is moving quickly to expand its sway in Central Asia, a region that was once in the Kremlin’s sphere of influence.

       Russia, for its part, is pushing back hard.

       As the leaders of Central Asian countries meet with the presidents of China and Russia this week in Astana, the capital of Kazakhstan, China’s rising presence is visible in the region. New rail lines and other infrastructure are being built, while trade and investment are rising.

       Flag-waving Kazakh children who sang in Chinese greeted Xi Jinping, China’s leader, upon his arrival in Astana on Tuesday. He praised ties with Kazakhstan as a friendship that has “endured for generations.”

       President Vladimir V. Putin of Russia arrived on Wednesday for the start of the gathering in Astana, an annual summit of the Shanghai Cooperation Organization, and he met with Mr. Xi, according to Xinhua, the state-run news agency.

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       The forum was for years focused largely on security issues. Beijing has come to dominate the group, and as it has expanded its membership, China and Russia have used it as a platform to showcase their ambitions of reshaping a global order dominated by the United States.

       The group, which was established by China and Russia in 2001 with the Central Asian countries Kazakhstan, Kyrgyzstan, Tajikistan and Uzbekistan, has expanded in recent years to include Pakistan, India and Iran.

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