Israel notified the NSA, where alarmed officials immediately began a hunt for the breach, according to people familiar with the matter, who said an investigation by the agency revealed that the tools were in the possession of the Russian government.

Israeli spies had found the hacking material on the network of Kaspersky Lab, the global anti-virus firm under a spotlight in the United States because of suspicions that its products facilitate Russian espionage.

Last month, the Department of Homeland Security instructed federal civilian agencies to identify Kaspersky Lab software on their networks and remove it on the grounds that “the risk that the Russian government, whether acting on its own or in collaboration with Kaspersky, could capitalize on access provided by Kaspersky products to compromise federal information and information systems directly implicates U.S. national security.” The directive followed a decision by the General Services Administration to remove Kaspersky from its list of approved vendors. And lawmakers on Capitol Hill are considering a governmentwide ban.