ASPEN, Colo. — It has been an open secret throughout the Obama presidency that world powers have escalated their use of cyberpower. But the recent revelations of hacking into Democratic campaign computer systems in an apparent attempt to manipulate the 2016 election is forcing the White House to confront a new question: whether, and if so how, to retaliate.

So far, the administration has stopped short of publicly accusing the Russian government of President Vladimir V. Putin of engineering the theft of research and emails from the Democratic National Committee and hacking into other campaign computer systems. However, private investigators have identified the suspects, and American intelligence agencies have told the White House that they have “high confidence” that the Russian government was responsible.

Less certain is who is behind the selective leaks of the material, and whether they have a clear political objective. Suspecting such meddling is different from proving it with a certainty sufficient for any American president to order a response.

Even if officials gather the proof, they may not be able to make their evidence public without tipping off Russia, or its proxies in cyberspace, about how deeply the National Security Agency has penetrated that country’s networks. And designing a response that will send a clear message, without prompting escalation or undermining efforts to work with Russia in places like Syria, where Russia is simultaneously an adversary and a partner, is even harder.