“Russia, if you’re listening, I hope you’re able to find the 30,000 emails that are missing,” Mr. Trump said at a news conference, referring to emails deleted from Mrs. Clinton’s private servers. On Monday, the White House spokesman, Sean Spicer, said during a briefing that Mr. Trump was “kidding” at the time.

As the official nominees of their parties, Mr. Trump and Mrs. Clinton began receiving intelligence briefings in early August. On Sept. 22, Democrats leading the House and Senate Intelligence Committees issued a statement accusing Russia “based on briefings we have received.” Four days later, during the first presidential debate, Mr. Trump declined to agree, adding that it could be China or “somebody sitting on their bed that weighs 400 pounds.”

On Oct. 7, the director of national intelligence and the Department of Homeland Security issued a joint statement saying they were “confident that the Russian government” had directed the cyberattacks.

Mr. Trump again expressed doubt that Russia was responsible. During the second presidential debate, he said, “Maybe there’s no hacking.”

His charge that Mr. Obama “did nothing” is also incorrect.

Though some Democrats were dissatisfied with Mr. Obama’s response and say his administration should have done more, Mr. Obama did act.

John O. Brennan, the former director of the Central Intelligence Agency, warned his Russian counterpart against meddling on Aug. 4, 2016, according to his testimony to Congress in late May. Around this time, the Department of Homeland Security also warned state governments of attempts to access voter registration systems and encouraged them to seek assistance, Jeh Johnson, the former Homeland Security secretary, has said.

In September, Mr. Obama warned Mr. Putin directly at a Group of 20 summit meeting in China. Mr. Obama confirmed at a news conference in December that he had told Mr. Putin to “cut it out,” and explained that he held back from retaliating for fear of Russia escalating the cyberattacks.