WASHINGTON — In the view of America’s spy services, the next potential threat from Russia may not come from a nefarious cyberweapon or secrets gleaned from the files of Edward J. Snowden, the former National Security Agency contractor now in Moscow.

Instead, this menace may come in the form of a seemingly innocuous dome-topped antenna perched atop an electronics-packed building surrounded by a security fence somewhere in the United States.

In recent months, the Central Intelligence Agency and the Pentagon have been quietly waging a campaign to stop the State Department from allowing Roscosmos, the Russian space agency, to build about half a dozen of these structures, known as monitor stations, on United States soil, several American officials said.

They fear that these structures could help Russia spy on the United States and improve the precision of Russian weaponry, the officials said. These monitor stations, the Russians contend, would significantly improve the accuracy and reliability of Moscow’s version of the Global Positioning System, the American satellite network that steers guided missiles to their targets and thirsty smartphone users to the nearest Starbucks.