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 Putin of engineering the theft of research and e-mails from the Democratic National Committee and hacking into other campaign computer systems. However, private investigators have identified the suspects, and US intelligence agencies have told the White House that they have “high confidence’’ that the Russian government was responsible.

But suspecting such meddling is different from proving it with a certainty sufficient for any US 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.

The Russians tried to make it tougher still Saturday when they declared that they had found evidence of US activity in their government systems.

It was hardly a shocking revelation; anyone who leafed through Edward J. Snowden’s revelations saw evidence of daily efforts to break into Russian spy agencies, nuclear installations, and leadership compounds.

But in a talk Friday evening at the Aspen Security Forum, an annual gathering that draws many of the nation’s top intelligence and military officials, CIA director John O. Brennan made clear that while spying on each other’s political institutions is fair game, making data public — in true or altered form — to influence an election is a new level of malicious activity, far different from ordinary spy vs. spy maneuvers.

“When it is determined who is responsible for this,’’ Brennan said, choosing his words carefully to avoid any direct implication of Russia, there “will be discussions at the highest levels of government about what the right course of action will be. Obviously, interference in the US election process is a very, very serious matter.’’

The Russia problem is thorny, and persistent. Just four months into his presidency in 2009, President Obama and his top national security advisers received a warning from US intelligence agencies: Of all the nations targeting America’s computer networks, Russia had the most “robust, longstanding program that combines a patient, multidisciplinary approach to computer network operations with proven access and tradecraft.’’

Obama might have been a bit distracted at the time. While setting up his new administration, he was also learning the dark arts of cyberwar, descending into the Situation Room to oversee a complex American-Israeli offensive operation to disable Iran’s nuclear centrifuges. He expressed concern to his aides that the operation would help fuel the escalation of cyberattacks and counterattacks.

The concern was justified. Since then, Iran has attacked Saudi Arabia, Russia has brought down a power grid in Ukraine, the North Koreans have attacked the South. The list gets longer every month.

But deterrence has been spotty. In the DNC case, two senior administration officials said midlevel officials were considering options, ranging from counter cyberattacks on the FSB and the GRU, two competing Russian spy agencies at the center of the current hacking, to economic, travel and other sanctions aimed at suspected perpetrators.

But each approach has downsides: A counterattack, for example, one senior official said, “brings us to their level, and their moral code.’’

Obama often says the world of cyberconflict is still “the Wild West.’’ There are no treaties, no international laws, just a patchwork set of emerging “norms’’ of what constitutes acceptable behavior.