Recent hacked emails are "consistent with the methods and motivation of Russia-directed efforts", the Department of Homeland Security said.
Data revealing discussions within the Democratic Party was hacked earlier this year.
Some states reported "probing" attempts made on "election-related" systems.
However, officials said those attempts could not be directly linked to the Russian government.
Russian officials told Interfax news agency the claims it was involved in the cyber attacks were "nonsense".