Israeli intelligence officials have caught Russian government hackers searching computers across the globe for classified American government secrets.

In a major revelation, Israel discovered that the Russians were using antivirus software made by the Kaspersky Lab company, which is used by 400 million people worldwide, to hunt for American intelligence programmes.

Israel’s technology experts managed to hack into Russian firm Kaspersky’s network two years ago and have subsequently warned their American counterparts about the problem.

Last month, as a result of the Israeli action, Washington ordered Kaspersky software to be removed from government computers.

This week reports in the American media revealed that the Israeli spies had also found hacking tools in Kaspersky's network that could only have come from the US National Security Agency (NSA).

And last month a classified US National Intelligence Council report, shared with NATO allies, concluded that Russia's FSB intelligence service had "probable access" to Kaspersky’s customer databases and source code.

There is still no public admission over what other US secrets the Russian hackers may have discovered by turning the Kaspersky software into a searchable database for sensitive information.

But it is claimed that the Russian operation stole classified documents from an NSA employee who had stored them on a home computer on which Kaspersky’s antivirus software was installed.

The NSA, White House and Israeli Embassy all declined to comment, the New York Times reported, while the Russian Embassy did not respond to requests for comment on the issue.

Last month Russia described the Washington ban on Kaspersky software “regrettable” and claimed it was problematic in moves to rebuild bilateral ties.

A Kaspersky spokeswoman told the US media “as a private company, Kaspersky Lab does not have inappropriate ties to any government, including Russia, and the only conclusion seems to be that Kaspersky Lab is caught in the middle of a geopolitical fight."

She denied any knowledge of the Israeli hack.