WASHINGTON — President Trump, who spent months belittling charges that Russia meddled in the 2016 election, has managed to revive questions about how his predecessor, President Barack Obama, handled suspicions about Russia in the months before the election.

Some former Obama officials now confess to misgivings about Mr. Obama’s reluctance to act, or speak out more forcefully, even as the evidence piled up during the spring and summer of 2016 that the Russians had hacked the Democratic National Committee and were behind the leak of damaging emails about Hillary Clinton.

Yet the officials say the indictment last week of 13 Russians by the special counsel, Robert S. Mueller III, does not suggest that Mr. Obama could have prevented the Russian campaign. The evidence uncovered in this phase of the investigation, they noted, is about Russia’s information warfare, not its hacking, and the government does not control what flows into the social media accounts of American citizens.

“If there was a problem, it was that the government didn’t have any levers to pull in this space,” said Benjamin J. Rhodes, a former deputy national security adviser and one of Mr. Obama’s closest aides. “The U.S. government isn’t designed to guard against the manipulation of every individual American’s Facebook feed and Twitter feed.”