WASHINGTON — The United States and its allies have dismantled a major cyberespionage system that it said Russia’s intelligence service had used for years to spy on computers around the world, the Justice Department announced on Tuesday.

In a separate report, the Cybersecurity and Infrastructure Security Agency portrayed the system, known as the “Snake” malware network, as “the most sophisticated cyberespionage tool” in the Federal Security Service’s arsenal, which it has used to surveil sensitive targets, including government networks, research facilities and journalists.

The Federal Security Service, or F.S.B., had used Snake to gain access to and steal international relations documents and other diplomatic communications from a NATO country, according to CISA, which added that the Russian agency had used the tool to infect computers across more than 50 countries and inside a range of American institutions. Those included “education, small businesses and media organizations, as well as critical infrastructure sectors including government facilities, financial services, critical manufacturing and communications.”

Top Justice Department officials hailed the apparent demise of the malware.

“Through a high-tech operation that turned Russian malware against itself, U.S. law enforcement has neutralized one of Russia’s most sophisticated cyberespionage tools, used for two decades to advance Russia’s authoritarian objectives,” Lisa O. Monaco, the deputy attorney general, said in a statement.

In a newly unsealed 33-page court filing from a federal judge in Brooklyn, a cybersecurity agent, Taylor Forry, laid out how the effort, called Operation Medusa, would take place.

The Snake system, the court documents said, operated as a “peer to peer” network that linked together infected computers around the world. Leveraging that, the F.B.I. planned to infiltrate the system using an infected computer in the United States, overriding the code on every infected computer to “permanently disable” the network.

The American government had been scrutinizing Snake-related malware for nearly two decades, according to the court filings, which said that a unit of the F.S.B. known as Turla had operated the network from Ryazan, Russia.

Even though cybersecurity experts identified and described the Snake network over the years, Turla kept it operational through upgrades and revisions.

The malware was difficult to remove from infected computer systems, officials said, and the covert peer-to-peer network sliced and encrypted stolen data while stealthily routing it through “numerous relay nodes scattered around the world back to Turla operators in Russia” in a way that was hard to detect.

The CISA report said Snake was designed in a way that allowed its operators to easily incorporate new or upgraded components, and worked on computers running the Windows, Macintosh and Linux operating systems.

The court documents also sought to delay notifying people whose computers would be accessed in the operation, saying it was imperative to coordinate dismantling Snake so the Russians could not thwart or mitigate it.

“Were Turla to become aware of Operation Medusa before its successful execution, Turla could use the Snake malware on the subject computers and other Snake-compromised systems around the world to monitor the execution of the operation to learn how the F.B.I. and other governments were able to disable the Snake malware and harden Snake’s defenses,” Special Agent Forry added.