House members Kathie Conway, Steve Cookson, Marsha Haefner and Nate Walker all released statements Tuesday saying Greitens should consider stepping aside.
Missouri Sen. Rob Schaaf also gave a speech Tuesday on the Senate floor, calling for Greitens to resign.
Walker was an early supporter of Greitens during his gubernatorial campaign. But Walker says the scandal doesn't appear to be going away, and Greitens should resign "so that that the state can move forward."
Several Democratic lawmakers also have called for Greitens' resignation.
Tuesday afternoon, Greitens posted to Facebook, asking for forgiveness and privacy.
The Republican governor has given no indication of resigning and has remained out of the public eye since acknowledging late Wednesday that he had been "unfaithful" to his wife. His attorney has denied more lurid allegations related to the affair.
KMOV-TV in St. Louis initially reported the affair. In the story, the ex-husband of the woman involved in the extramarital affair claimed Greitens blindfolded the woman, led her downstairs and then took a picture of her, which the ex-husband says Greitens then used for blackmail.
The identities of the woman and ex-husband were not released in KMOV’s report. The woman allegedly involved did not comment on the record to the station, but her ex-husband provided an audio recording he made to KMOV in which a woman gives details about a sexual encounter.
The ex-husband claimed she was talking about herself and Greitens when she went to the Greitens’ St. Louis home in March 2015. The woman did not know her then-husband was recording their conversation.
Several other St. Louis media outlets, including Fox 4’s sister station Fox 2, also had the recording, but chose not to release it because the woman refused to comment. Once the recording became public, those St. Louis outlets felt compelled to release it as well.
Greitens' attorney James Bennett said any allegations of violence are false, and the relationship was consensual.
“This was a consensual relationship that lasted multiple months and was years ago before Eric was elected Governor,” Bennett said.
Bennet said Thursday that they believe the report was the result of a “political hit piece.”
“The latest reporting has finally disclosed that the reporting was being driven by a ‘source’ who is the former Democrat state party chairman and who apparently has not spoken to the person in question,” Bennett said. “This goes a long way to explaining what is going on. It’s become clear this is a political hit piece. This is and remains an almost three-year-old private matter with no matter of public interest at stake.”
On Thursday, some groups and individuals began calling for Greitens’ resignation. But Bennett said the governor will not resign.
“The governor is not resigning and his plans are to continue to serve the people of Missouri,” Bennett said Thursday.
A St. Louis circuit attorney said Thursday she has launched an investigation to determine if Greitens committed crimes.
On Friday, a St. Louis-area attorney has released a statement, asking for privacy on behalf of the unnamed woman. Read the full statement here.