MOSCOW — The deputy prime minister in charge of Russia’s space programs said Sunday that he had started to impose restrictions on Global Positioning System base stations here, as retribution for the refusal of the United States to allow similar base stations on American territory that would improve the accuracy of Russia’s navigation system.

The restrictions will not cause any disruption in the operation of GPS, as the American satellite navigation system is more commonly known. Still, they are a sign of how deeply soured relations have become between the United States and Russia in the months since the Kremlin’s annexation of Crimea, and other long-simmering disputes, including Russia’s granting of asylum to Edward J. Snowden, the fugitive national security contractor.

The deputy prime minister, Dmitri O. Rogozin, said that as of Sunday the GPS base stations in Russia could not be used for military purposes, and he announced a deadline of Sept. 1 for the United States to agree to allow base stations on its territory for Russia’s navigation system, Glonass. Otherwise, he said, the GPS terminals would be shut down for good.

“We have worked out and implemented measures that exclude the use of these [GPS] stations for military purposes,” Mr. Rogozin wrote in a blog post. “Now they are under our full control.”