MOSCOW — Russia’s deputy prime minister in charge of space programs said Sunday he had started to impose restrictions on GPS base stations here, as retribution for the U.S. refusal to allow similar base stations on U.S. territory that would make Russia’s navigation system more accurate.

The restrictions will not disrupt any of the operation of GPS.

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 Russia’s granting of asylum to Edward Snowden, the fugitive U.S. national-security contractor.

The deputy prime minister, Dmitry Rogozin, said that as of Sunday the GPS base stations in Russia could not be used for military purposes.

He also announced a Sept. 1 deadline 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.

Rogozin is one of the most prominent Russian officials to be sanctioned by the United States over President Vladimir Putin’s policies toward Ukraine.

He recently suggested that U.S. astronauts may no longer be carried on Russian spacecraft to the international space station.