KHIVA, Uzbekistan — Inside the ancient walls of the Silk Road oasis town of Khiva, China has put down a marker of its geopolitical ambitions. A sign promotes a Chinese aid project to renovate a once-crumbling mosque and a faded madrasa.

Outside the town’s northern gate, a billboard-size video screen shows clips of President Shavkat Mirziyoyev of Uzbekistan meeting with world leaders. President Xi Jinping of China features prominently, but there are no shots of President Trump.

That China is advertising its aid efforts so boldly in this remote outpost linking Asia and Europe — where camel caravans once arrived after crossing the Kyzylkum and Karakum Deserts — is the kind of action these days that sets off alarm bells among American officials. The Trump administration is trying with greater force to insert itself into the political and economic life of Central Asia to counter China’s presence. American officials see the countries in the heart of the continent’s vast, arid steppe as critical battlegrounds in the struggle with China over global influence.

“Whenever we speak to countries around the world, we want to make sure that we’re doing what the people of those countries want,” Secretary of State Mike Pompeo said last week at a news conference in Tashkent, the capital of Uzbekistan.