"None of the threats have been determined to be credible thus far," the FBI said in a statement, adding that election integrity was among the bureau's highest priorities.
At least two polling sites targeted by the hoax bomb threats in the election battleground state of Georgia were briefly evacuated on Tuesday.
Those two locations in Fulton County both re-opened after about 30 minutes, officials said, and the county is seeking a court order to extend the location's voting hours past the statewide 7 p.m. deadline.
Republican Georgia Secretary of State Brad Raffensperger blamed Russian interference for the Election Day bomb hoaxes.
"They're up to mischief, it seems. They don't want us to have a smooth, fair and accurate election, and if they can get us to fight among ourselves, they can count that as a victory," Raffensperger told reporters.
The Russian embassy in Washington did not immediately respond to a request for comment.
In a statement, the FBI said it was aware of non-credible bomb threats to polling locations in several states, with many of them originating from Russian email domains.
Georgia alone received more than two dozen phony bomb threats on Election Day, most of which occurred in Fulton County, an FBI official said.
A senior official in Raffensperger's office, speaking on the condition of anonymity to speak freely, said the Georgia bomb hoaxes were sent from email addresses that had been used by Russians trying to interfere in previous US elections.
The threats were sent to US media and the two polling locations, the official said. "It's a likelihood it's Russia," the official said.
Democratic Vice President Kamala Harris and Republican former President Donald Trump are locked in a tight race to win the White House. Opinion polls suggest the contest is too close to call.
The phony bomb threats mark the latest in a string of examples of alleged interference by the Russians in the 2024 election.
On November 1, US intelligence officials warned that Russian actors manufactured a video that falsely depicted Haitians illegally casting ballots in Georgia. Intelligence officials also found that the Russians created a separate phony video which falsely accused someone associated with the Harris presidential ticket of taking a bribe from an entertainer.
US intelligence officials have also accused Russia of interfering in previous US presidential elections, especially the 2016 race which Trump won against Democratic candidate Hillary Clinton.
