In his first interview since acknowledging an extramarital affair, Governor Eric Greitens of Missouri said on Saturday there was “no blackmail” and “no threat of violence” by him in what he called a months-long “consensual relationship” with his former hairdresser.

The Republican, who was a US Navy Seal before entering politics, has remained out of the public eye since shortly after delivering his state of the state address on 10 January.

Later that night, St Louis television station KMOV reported that Greitens had an extramarital affair in 2015 as he was preparing to run for governor.

The report included an audio recording of a conversation between a woman and her then husband – recorded secretly by the husband – in which the woman said Greitens had bound her hands and blindfolded her, taken a photo of her partially nude and warned her to remain silent during an encounter in his home.

Grietens did not directly say “yes” or “no” when asked on Saturday if he had bound and blindfolded and taken a photo of the woman. But he firmly denied that he had attempted to coerce the woman.

Eric Greitens and his wife Sheena speak to the media in St Louis. Photograph: Jeff Roberson/AP

“This was a consensual relationship,” Greitens said. “There was no blackmail, there was no violence, there was no threat of violence, there was no threat of blackmail, there was no threat of using a photograph for blackmail. All of those things are false.”

Greitens added: “The mistake that I made was that I was engaged in a consensual relationship with a woman who was not my wife. That is a mistake for which I am very sorry.”

Greitens said he had no plans to resign from office as a result of the affair, despite calls to step aside from several Republican and Democratic state lawmakers.

“I’m staying. I’m staying,” he said twice for emphasis, adding about his relationship with his wife, staff and supporters: “We’re strong.”