ASTANA, Kazakhstan — Russian President Vladimir Putin and Chinese President Xi Jinping hailed their Eurasian security club on Wednesday as a force for global stability at a summit of the regional body, which is seen by Moscow and Beijing as a tool to counter Western influence.

Putin and the Chinese president have expanded the Shanghai Cooperation Organization (SCO), a club founded in 2001 with Russia, China and Central Asian nations, to include India, Iran and Pakistan as a counterweight to…