While Chinese hacking groups are known for sweeping up vast amounts of commercial and design information, the best Russian hackers tend to hide their tracks better and focus on specific, often political targets. And the hacking happened at a moment of renewed tension with Russia — over its annexation of Crimea, the presence of its forces in Ukraine and its renewed military patrols in Europe, reminiscent of the Cold War.

Inside the White House, the intrusion has raised a new debate about whether it is possible to protect a president’s electronic presence, especially when it reaches out from behind the presumably secure firewalls of the executive branch.

Mr. Obama is no stranger to computer-network attacks: His 2008 campaign was hit by Chinese hackers. Nonetheless, he has long been a frequent user of email, and publicly fought the Secret Service in 2009 to retain his BlackBerry, a topic he has joked about in public. He was issued a special smartphone, and the list of those he can exchange emails with is highly restricted.

When asked about the investigation’s findings, the spokeswoman for the National Security Council, Bernadette Meehan, said, “We’ll decline to comment.” The White House has also declined to provide any explanations about how the breach was handled, though the State Department has been more candid about what kind of systems were hit and what it has done since to improve security. A spokesman for the F.B.I. declined to comment.

Officials who discussed the investigation spoke on the condition of anonymity because of the delicate nature of the hacking. While the White House has refused to identify the nationality of the hackers, others familiar with the investigation said that in both the White House and State Department cases, all signs pointed to Russians.

On Thursday, Secretary of Defense Ashton B. Carter revealed for the first time that Russian hackers had attacked the Pentagon’s unclassified systems, but said they had been identified and “kicked off.” Defense Department officials declined to say if the signatures of the attacks on the Pentagon appeared related to the White House and State Department attacks.

The discovery of the hacking in October led to a partial shutdown of the White House email system. The hackers appear to have been evicted from the White House systems by the end of October. But they continued to plague the State Department, whose system is much more far-flung. The disruptions were so severe that during the Iranian nuclear negotiations in Vienna in November, officials needed to distribute personal email accounts, to one another and to some reporters, to maintain contact.