Germany's BSI, which also uses Kaspersky products for technical analyses, said it was in touch with US officials and other security agencies about the issue so it could take action and issue a warning on short notice if required.
The US government banned the use of Kaspersky software in federal offices last month, saying the Moscow-based company has risky ties to Russian intelligence that threatened US national security.
Israeli agents made the discovery after breaching the software themselves.
Last month, the USA government chose to stop using the Russian firm's software on its computers.
After an investigation, the NSA found that those tools were in possession of the Russian government, the Post said.
The firm added that it has never helped, nor would help, governments in matters of cyber-espionage. The anti-virus vendor is used by 400 million people globally, including United States government agencies.
In antivirus "Kaspersky Lab" was spelled out an in depth scan documents on the computers to search for classified information.
Kaspersky Lab has repeatedly denied any knowledge of, or involvement in, Russian hack1ing.
The NSA, the White House and the Israeli embassy in Washington have not commented on the matter.
The New York Times said that the situation had been described by "multiple people who have been briefed on the matter".
The New York Times said that the Russian embassy had not responded to a request for comment.
Kaspersky Lab has been the target of growing hostility within the U.S., primarily based on the fact it is a Russian-base company. Eugene Kaspersky, its founder trained at a KGB-funded institute.
In a statement at the time of The Wall Street Journal article, Kaspersky said: As a private company, (we do) not have inappropriate ties to any government, including Russian Federation, and the only conclusion seems to be that Kaspersky Lab is caught in the middle of a geopolitical fight.