U.S. officials suspect Russian hackers were responsible for breaking into two state election databases earlier this month.
"This is the closest we've come to tying a recent hack to the Russian government," one official told NBC News on Monday.
The FBI has not identified the two U.S. states whose data bases were attacked, but Yahoo News, which first reported the breaches, quoted sources who say Arizona and Illinois were targeted.
According to Yahoo News, an Illinois election board official said the voter registration system was shut down for 10 days last month after hackers stole personal information on approximately 200,000 voters.
The Arizona attack involved the introduction of malicious software into the voter registration system.
The FBI is urging local law enforcement officials to enhance their computer security systems.
U.S. officials have said recent cyberattacks at the Democratic National Committee and elsewhere within the Democratic Party probably were conducted by people inside the Russian government. Russia has denied any involvement in the cyberattacks.
Federal officials are becoming increasingly concerned about the possibility that hackers, particularly those working for Russia, could breach U.S. elections systems and wreak havoc on the November presidential election.