The administration has not publicly criticized how its own officials handled the case. But the Times investigation revealed that the F.B.I. first informed the Democratic National Committee that it saw evidence that the committee’s email systems had been hacked in the fall of 2015. Months of fumbling and slow responses followed.

Mr. Obama said at a news conference that he was first notified early this summer. But one of his top aides met Russian officials in Geneva to complain about activity in April.

By the time the leadership of the committee woke up to what was happening, the G.R.U. had not only obtained emails through a hacking group that has been closely associated with it for years, but, investigators say, also allowed them to be published on a number of websites, including a newly created one called DC Leaks and the far more established WikiLeaks. Meanwhile, several states reported the “scanning” of their voter databases — which American intelligence agencies also attributed to Russian hackers. But there is no evidence, American officials said, that Russia sought to manipulate votes or voter rolls on Nov. 8.

Mr. Obama decided not to issue sanctions earlier for fear of Russian retaliation ahead of Election Day. Some of his aides now believe that was a mistake. But the president made clear before leaving for Hawaii that he planned to respond.