The FBI has been asked to investigate whether a hoaxer offered women money to make false allegations about Robert Mueller, the special counsel investigating Russia’s interference in the 2016 election.

Several journalists and bloggers in the US received an email this month purporting to be from a woman who had been offered money to smear Mueller with bogus claims of inappropriate behaviour decades ago.

After Mueller’s office was told about the email, it referred the matter to federal investigators, who are now likely to examine whether the hoax scheme described in the woman’s email is real – or if the email itself contains false information.

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Peter Carr, Mueller’s spokesman, said in a statement on Tuesday: “When we learned last week of allegations that women were offered money to make false claims about the special counsel, we immediately referred the matter to the FBI for investigation.”

This statement itself was rare for Mueller’s office, which has built a reputation over the past 17 months for almost never making public remarks about its activities outside of court hearings and legal filings.

Mueller has come under sustained pressure from Donald Trump and some Republicans in Congress, who have tried to dismiss his investigation as a “witch-hunt”. Mueller has so far obtained criminal convictions of Trump’s former campaign chairman Paul Manafort for financial crimes, along with guilty pleas from several people including Mike Flynn, Trump’s former national security adviser, and Rick Gates, his former deputy campaign chairman.

The sender of the email to journalists and bloggers claimed to be a woman in Florida who had worked with Mueller at a law firm in the 1970s. She said she had been offered $30,000 and other benefits to make false allegations against Mueller. But, she said, Mueller was in fact “always very polite to me, and was never inappropriate”.

The woman identified herself by a name that could not be matched with public records and efforts by journalists to contact her were unsuccessful.

She also said she was told the man behind the scheme was named Jack Burkman. A rightwing talk radio host with that name, who has pushed discredited conspiracy theories in the past, has publicly claimed to know of similar allegations about Mueller.

Burkman, who is also a registered lobbyist in Washington, has in the past raised money to help pay the legal fees of Rick Gates, Donald Trump’s former deputy campaign chairman, who pleaded guilty to conspiracy and lying to the FBI.

Gates recorded a thank-you video message for a fundraiser held by Burkman in Virginia in December 2017, where Burkman described him as “our good friend Rick”. In his message, Gates said: “Jack, thank you for your work, your commitment and your dedication.”

News of the video message prompted the judge in Gates’s case to demand that he explain “the nature of his relationship” with Burkman. Attorneys for Gates confirmed that “he knows” Burkman but said he had “not physically met with him”. An attorney for Gates did not immediately respond to an email on Tuesday.