A formal investigation into the allegations is being launched, Kimberly M. Gardner, circuit attorney for the city of St. Louis, announced Thursday.
"The Governor is very confident he will be cleared in any investigation," Greitens' lawyer, James Bennett, said. "This is a three-year-old personal matter that presents no matters of public or legal interest. The facts will prove that fully. As we learned today, these false allegations are being advanced by political adversaries."
CNN affiliate KMOV published an investigation
Wednesday night alleging that Greitens, who is married, had a sexual relationship with an unidentified woman. The woman's ex-husband cooperated with KMOV, providing what he said was a recording from 2015 of his former wife describing in detail disturbing interactions she had with Greitens. Greitens was elected to office in 2016.
In the recording aired by KMOV, the woman says she went to Greitens' house, where a sexual encounter took place.
"And he used some sort of tape, I don't what it was, and taped my hands to these rings and then put a blindfold on me," she said in the recording, recalling that Greitens told her that "'you're never going to mention my name,' otherwise there will be pictures of me (the woman) everywhere."
In the recorded conversation, the woman said Greitens apologized to her afterwards and told her he had deleted the picture, KMOV reported.
"He took a picture of my wife naked as blackmail. There is no worse person," the ex-husband told the station.
In a series of statements Wednesday night and Thursday morning, Greitens pushed back on key allegations from the woman's ex-husband. "There was no blackmail and that claim is false," Bennett said in a statement.
"This personal matter has been addressed by the Governor and Mrs. Greitens privately years ago when it happened," Bennett said. "The outrageous claims of improper conduct regarding these almost three-year-ago events are false."
Answering multiple follow-up questions from CNN, Bennett clarified that the governor explicitly denies taking a photo of the woman and suggesting that he could make the photo public. Bennett also said there was no settlement between the governor and the woman, and that there was never a non-disclosure agreement.
Asked whether the governor has been previously accused of misconduct by anyone else other than this woman in question, Bennett responded, "No."
The governor released a joint statement with his wife, Sheena, Wednesday night, saying that, years before he was elected governor, "there was a time when he was unfaithful in our marriage."
"This was a deeply personal mistake. Eric took responsibility, and we dealt with this together honestly and privately. While we never would have wished for this pain in our marriage, or the pain that this has caused others, with God's mercy Sheena has forgiven and we have emerged stronger," according to the couple's statement.
The news of the extramarital affair and allegations of blackmail came on the same night that Greitens delivered the State of the State speech.
State legislative leaders from both parties reacted to the KMOV's report with dismay.
"Like many Missourians, we find these serious allegations shocking and concerning. As this situation is evolving, we expect the governor to be honest and forthright," said Republican state Sens. Ron Richard, Mike Kehoe and Bob Onder in a joint statement.
"In light of the very serious allegations made against the governor, there are many questions still left unanswered. But let's be clear -- violence and threats against women are never acceptable," their Democratic leadership counterparts, state Sens. Gina Walsh and Kiki Curls, said in a joint statement. "Allegations of extortion, coercion or threats of violence must be investigated by the proper authorities. People accused of these egregious acts do not get to waive off the scrutiny of law enforcement simply because they are in a position of power; and victims of these crimes deserve our full support."
Greitens campaigned in 2016 as a political outsider. The former Navy Seal and his wife married in 2011 and have two children.
"We have a loving marriage and an awesome family; anything beyond that is between us and God," Sheena Greitens said in an additional statement. "I want the media and those who wish to peddle gossip to stay away from me and my children."
As governor, Greitens has alienated some state lawmakers in his own party with sometimes scathing criticism of the legislature. But that approach has also helped him to cultivate a reputation among the national party as a promising prospect. He traveled to Iowa last year, stoking speculation about his national political ambitions
This story has been updated.