Suspicious envelopes, some laced with fentanyl, have been sent to election offices in at least five US states.
The letters were reported in Georgia, Nevada, California, Oregon and Washington, where the letter included a warning to "end elections now".
Georgia Secretary of State Brad Raffensperger described the letters as "domestic terrorism" that "needs to be condemned".
Fentanyl is a synthetic painkiller 50 times more powerful than heroin.
It has been blamed for a rise in US drug deaths.
According to the FBI and US Postal Service, fentanyl was found in four of the letters. Some of the letters were intercepted before they arrived at their final destination.
"Law enforcement is working diligently to intercept any additional letters before they are delivered," the FBI and Postal Service said in a statement.
In Washington, officials in Pierce County released images of a letter - postmarked in Portland, Oregon - which included the words "end elections now".
A similar letter was received in Seattle's King County, which reported another fentanyl-laced letter during an August primary election.
In Georgia, the letter appeared to be targeting an office in Fulton County. Authorities discovered the letter and found it contained fentanyl.
"Some people like to call fentanyl a drug," Mr Raffensperger told reporters on Thursday. "It's actually poison, it will kill you, it will kill you very quickly, very easily."
"My wife and I lost our son five-and-a-half years ago due to a fentanyl overdose, we know how deadly this stuff is."
Brenton Raffensperger died in 2018 aged 38.
In Washington, election offices in four counties - King, Pierce, Skagit and Spokane - received envelopes containing "unknown powdery substances", according to Secretary of State Steve Hobbs.
The incidents took place as workers were counting ballots from the 7 November general election, said Mr Hobbs, a Democrat.
"These incidents are acts of terrorism to threaten our elections," he said, echoing Mr Raffensperger.
The Postal Service was able to intercept envelopes headed to Los Angeles and Sacramento, according to the Associated Press.
Fulton County in Georgia has been the target of repeated unfounded claims by former President Donald Trump of widespread ballot fraud.
He is now facing charges in that same county for allegedly conspiring to overturn Georgia's vote results from 2020.
Mr Trump has pleaded not guilty.
On Wednesday, Fulton County Commission Chairman Robb Pitts - a Democrat - said that officials there had been under threat since the 2020 election.
He added that there are "people out there who want to do harm to our workers and disrupt, interrupt, the flow of democracy".
Mr Pitts added that officials are prepared for the 2024 election, which he said would be the "focal point" of tension and scrutiny.
"This was a good trial run for us," he said.