CNN earlier reported citing US officials that Russian hackers were "behind the damaging cyber intrusion of the State Department in recent months used that perch to penetrate sensitive parts of the White House computer system."
The hackers believed to be "working for the Russian government" had access to information on real-time non-public details of the US president's schedule, although such information is not classified, the report said.
Meanwhile, Rhodes refused to confirm that the Russian hackers were behind the cyber-attacks, but said: "It's fair to say ... Russia has been active in the cyber space and in the espionage space."
He failed to detail when these attacks occurred. The official also stressed that the activity of other countries in this sphere, including Iran, causes concern in the United States.
National Security Council spokesperson Mark Stroh told journalists the incident came to light last year. "Any such activity is something we take very seriously," he added.