The United States believes that it must have a sizable military base in Central Asia to support the NATO mission in Afghanistan, especially now that supply routes through Pakistan are perilous. The American installation on the outskirts of the Kyrgyz capital is crowded with C-17 cargo planes and KC-135 tanker planes that readily reach the Afghan skies for mid-air refueling of fighters. As many as 30,000 military personnel cycle through the base monthly.

Those troops and planes have stirred deep unease in the Kremlin, which tried to persuade Mr. Bakiyev to oust the Americans, in the end unsuccessfully. Central Asia is Moscow’s former territory and current backyard, and the Kremlin evinces a sense of entitlement here, not to mention a desire to dominate natural resources.

At the same time, the Russians seem torn over the American venture in Afghanistan. They understand that failure could threaten even Russia, which has grappled with Islamic extremism in its south, so they have allowed American military goods to flow across Russia. The Kremlin also can sympathize with Washington’s plight, given painful memories of the Soviet involvement in Afghanistan.

Still, the Kremlin fears that the United States is setting down lasting roots in Central Asia.

Russia’s role in the former Soviet republics has been a constant source of friction between the two sides. Just last week, Vice President Joseph R. Biden Jr. visited Ukraine and Georgia and rebuked Russia for its “19th-century notion of spheres of influence.”

The other major player in Central Asia is China, which is also wary of the spread of Muslim fundamentalism. The Chinese concerns were underscored in recent weeks by the uprising by Uighurs, a Muslim ethnic group, in the Chinese region that borders Central Asia. Chinese companies are also investing billions of dollars in Central Asia.