The hackers may have gained access to White House data through an earlier intrusion at the State Department, where officials regularly use e-mail to communicate with colleagues, according to U.S. officials who spoke on condition of anonymity.

"As we made clear at the time, we took immediate measures to evaluate and mitigate the activity," Mark Stroh, a National Security Council spokesman, said in an e-mail.

Russian Response

The Russian embassy in Washington didn't immediately respond to a phone call seeking comment. Earlier, Russia rejected a report by CNN Tuesday that its government was involved in hacking a non-classified White House computer network that exposed sensitive parts of the e-mail system.

"It has become a kind of sport to blame everything on Russia," Kremlin spokesman Dmitry Peskov told reporters on a conference call on Wednesday. "But the key thing is that they wouldn't go searching for Russian submarines in the Potomac River, like it was the case in some other countries."

Deputy White House National Security Adviser Ben Rhodes said Tuesday on CNN that no classified information had been compromised, while declining to link any attacks to Russia.

U.S. intelligence officials say the pace and sophistication of Russian-sponsored attacks have increased as tension over Ukraine has grown and the U.S. has imposed economic sanctions on Russia.

–With assistance from Angela Greiling Keane in Washington.