While the last option is tempting, officials say, it would carry risks with the election just a month away. Attacks on online voter registration rolls could sow chaos at polling places, and the election infrastructure has never truly been tested against a power like Russia. The system that underpins American democracy is not even listed as an element of the nation’s critical infrastructure, a list that includes movie theaters and the Jefferson Memorial, among other monuments.

Just as Henry Kissinger and other American strategists argued decades ago whether it was possible to wage a limited nuclear war, officials at the Pentagon and intelligence agencies, as well as outside experts, have been debating whether it is possible to control the escalation of a cyberconflict.

In the nuclear era, seven decades passed with no answer, despite some close calls. Online, where the damage is less lethal but cheap, and attacks are hard to trace and easy to carry out, Mr. Obama and other top officials are proceeding cautiously. Well-armed cyberpowers face few limits to their ability to escalate attacks. And it is unclear how the United States can establish what the generals call “escalation dominance” — the assurance that America can ultimately control how a conflict ends.

Michael J. Morell, a former deputy director of the C.I.A. and a veteran of many debates on the growing cyberweapon arsenal in the Bush and Obama administrations, said on Saturday that the American response had to strike at something that Mr. Putin held dear. But, he added, unleashing a counterattack may not be the answer.

“Our response needs to be proportionate to the attack,” said Mr. Morell, who now advises Hillary Clinton on national security matters and is widely believed to be in line for a top intelligence post if she is elected president. Criminal indictments and sanctions against individuals “are only a slap on the wrist,” he said, adding that “offensive cyberactions can’t be seen and are inconsistent with the norms we want to set in the world on cyber.”