It did not name President Vladimir V. Putin of Russia, but that appeared to be the intention.

The statement from Mr. Clapper and the Department of Homeland Security, which is primarily responsible for defending the country against sophisticated cyberattacks, said the intelligence agencies were less certain who was responsible for “scanning and probing” online election rolls in states around the country. It said that those “in most cases originated from servers operated by a Russian company,” but stopped short of alleging the Russian government was responsible for those probes.

The announcement came only hours after Secretary of State John Kerry called for the Russian and Syrian governments to face a formal war-crimes investigation over attacks on civilians in Aleppo and other parts of Syria. Taken together, the developments mark a sharp escalation of Washington’s many confrontations with Moscow this year.

For weeks, aides to Mr. Obama have been debating whether to openly attribute the cyberattacks to Russia, and as recently as Wednesday the director of the National Security Agency, Adm. Michael Rogers, refused to publicly accuse Moscow.

But with little more than a month to go before the presidential election, one senior administration official said that Mr. Obama was “under pressure to act now,” in part because a declaration closer to Election Day would appear to be political. Two days ahead of the second presidential debate, the announcement also puts the Republican nominee, Donald J. Trump, more on the defensive over his assertion last month that Mr. Putin is a better leader than Mr. Obama.

In the first debate, former Secretary of State Hillary Clinton, Mr. Trump’s Democratic rival, blamed Russia for the cyberattacks on the Democratic National Committee, but Mr. Trump said there was no evidence that Russia was responsible; he suggested it could have been the Chinese or “somebody sitting on their bed that weighs 400 pounds.”