Earlier this year, Russian hackers attempted to penetrate Democratic party email accounts in California and Indiana.
They would also have attacked at least five think tanks. The hackers would have failed to get in.
The Reuters news agency reports based on sources surrounding the investigation that the hacking attempts were the work of the hacker group Fancy Bear.
This is associated with the Russian military intelligence service GROe. Fancy Bear was also seen as the perpetrator of the Democratic mail account hack in the US presidential election four years ago.
The Democrats in Indiana say they are unaware of successful attacks.
The party members in California say there has been a failed attack attempt by a “foreign group”, but do not name them. The FBI and the security arm of tech company Microsoft do not want to respond.