The governor, who billed himself as a values-based family man, said in a statement that being unfaithful in his marriage was a "deeply personal mistake".
St. Louis TV station KMOV had obtained in which the woman, his hairstylist, discussed intimate details of the relationship, which took place in 2015, and said that Greitens at one point blindfolded her and took a picture of her partly unclothed, bound, and blindfolded, which he meant to use as blackmail.
The woman involved did not comment on the record to the TV station, which did not name her.
Following Greitens' denial of blackmail, the allegations are growing worse.
The woman met Greitens because she cut his hair. She did not return a call to the salon where she works, and an AP reporter who went there was told the hairdresser was not working.
She says every woman in the General Assembly should "rise up and do the right thing".
In response, Greitens' attorney stated that his client had a months-long consensual relationship (prior to his election as governor, although that doesn't matter) with the mistress but that "there was never any violence".
A Democrat-turned-Republican, Greitens, 43, was elected governor in November 2016 after a campaign that emphasized his status as a family man.
She also said, "as hard it is not just to want to drop in and say, 'Throw him out.' I don't want to do that".
"Eric took responsibility, and we dealt with this honestly and privately", the statement continued.
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Republican leaders in the Missouri Senate and House released statements urging Greitens to be "forthright" and "accountable for his actions". McCann Beatty said it's unfortunate that Greitens didn't address the concerns of protesters in St. Louis, who took to the streets after a white former police officer was acquitted in September in the 2011 shooting death of a black suspect.
Bennett, in an email to Reuters, dismissed the Circuit Attorney's investigation, calling the blackmail claim "false allegations" advanced by political opponents.
He thanked "God's mercy" for helping his wife Sheena forgive him.
A lawyer for Greitens denied the blackmail allegations. "I want the media and those who wish to peddle gossip to stay away from me and my children", Sheena Greitens said in a separate message. "The outrageous claims of improper conduct regarding these nearly three-year-ago events are a lie".
The governor released a series of statements to the media. "We understand that there will be some people who cannot forgive - but for those who can find it in your heart, Eric asks for your forgiveness, and we are grateful for your love, your compassion, and your prayers".
"If they feel that it's warranted, we definitely need to do that because otherwise I think there will be a cloud hanging over the whole governor's seat", said Redmon. "These alleged actions have cast another dark shadow over the Missouri State Capitol".
"The Governor denies that the picture was taken and denies stating the words attributed to him by her on the recording". This is a three-year-old personal matter that presents no matters of public or legal interest. She declined an interview request from the Post-Dispatch.
As to whether Greitens will still attend the convention or speak, "that is a decision that he and his wife will have to make in the coming weeks as they figure out how best to move forward", Brooks said.
Though Greitens has had his moments of success as governor, like signing a right-to-work law early previous year, he was fined $1,000 after admitting to the Missouri Ethics Commission that he had violated campaign finance law, according to the Kansas City Star.