A press release by The Case Breakers claimed to have identified the notorious serial killer as Gary Francis Porte, who died in 2018.
The group of 40 former professional investigators and forensic specialists also said that they have evidence linking him to a 1966 murder in Southern California, therefore adding to the official death toll of the Zodiac Killer.
However, the FBI says they should hold odd making such claims.
“The case remains open and there is no new information to report,” the bureau said.
Zodiac terrorised the San Francisco Bay Area in the late 1960s, slaying five people by targetting couples (two men survived) and murdering a lone taxi driver.
He famously sent coded letters and ciphers to the authorities via The San Francisco Chronicle, baiting the police to find him. He was never caught or identified.
The Case Breakers identified Mr Porte based on a trove of photographs showing a scar that matched a police sketch of Zodiac, interviews with people who knew him, and a number of pieces of evidence from the unsolved murder of Cheri Jo Bates in 1966.
Ms Bates was killed two years before Zodiac was known to be active, hundreds of miles to the south of the Bay Area in Riverside, California.
Officer Ryan Railsback of Riverside’s police department told NBC News that any connection between Ms Bates’ murder and the Zodiac Killer has been unequivocally ruled out.
“We don’t know how we can be any more clear,” he said on Wednesday, noting that a $50,000 private reward was still valid if anyone has information relating to the case.
Mr Railsback also told the Chronicle: “Is there a chance that [the Case Breakers suspect] killed Cheri Jo Bates? No.”
He added: “If you read what they put out, it’s all circumstantial evidence. It’s not a whole lot.”
An anonymous letter received months after Ms Bates’ murder that had at one point tied the case to the Zodiac Killer was found to be a hoax after investigators received a second message fifty years later in 2016 admitting it was a “sick joke”.
The case of the Zodiac Killer has long been a source of intense fascination spawning books, documentaries, TV shows, and movies.
Of the four ciphers he included in his messages, only two have ever been solved — one in 1969 and one by amateur sleuths in 2020.
Neither provided a break in the investigation to identify the killer.