JEFFERSON CITY – Facing new calls from some fellow Republicans to resign, Missouri Gov. Eric Greitens instead affirmed his intent Tuesday to remain on the job while seeking forgiveness for an extramarital affair that he described as a "personal mistake."

Greitens, who has stayed out of the public eye since admitting to an affair last week, distributed a message via Facebook and email Tuesday that simultaneously apologized for his actions and asserted that some allegations against him were false and "extremely hurtful."

"I assure you that this personal mistake will not deter us from the mission we were sent here to do," Greitens said in the statement. "We have been, and we will, continue to work for and to fight for the people of Missouri."

Greitens issued the statement as Republican Sen. Rob Schaaf, of St. Joseph, was calling upon him to resign during a speech on the Senate floor.

"When you ran for office, you promised that you would be a governor known for ethics and transparency," said Schaaf, directing his comments as if Greitens was there listening. "Instead, you have defined yourself through scandal and covering things up."

Schaaf concluded: "So governor, I'm asking you: please resign."

State Reps. Nate Walker or Kirksville, Marsha Haefner of Oakville, Steve Cookson of Poplar Bluff and Kathie Conway of St. Charles all also called for Greitens to step down Tuesday. Several Democrats also have called for the governor's resignation.

"For our state to continue to move forward, I think it's time for new leadership there in the governor's office," Walker, an early supporter of Greitens, told The Associated Press.

Jim Bennett, Greitens' private attorney, said the governor will not resign.

St. Louis television station KMOV reported Jan. 10 that Greitens had an affair with his St. Louis hairdresser in 2015 as he was preparing to run for governor. Greitens acknowledged the affair in a statement minutes after the report. But Bennett later denied the woman's claim to her now ex-husband – recorded without her knowledge during a March 2015 conversation – that Greitens took a compromising photo to ensure her silence.

St. Louis Circuit Attorney Kim Gardner announced a criminal investigation on Thursday, citing "serious allegations" against Greitens, 43, a former Navy SEAL officer who defeated Democratic Attorney General Chris Koster in the November 2016 gubernatorial race.

The woman has declined to speak publicly, and The Associated Press is not naming her. Bennett said Greitens did not reach a financial settlement with the woman, and there is no non-disclosure agreement.

Greitens' affair has been a disruption as Missouri lawmakers start the 2018 legislative session.

The House has delayed a vote on a Greitens-backed ethics bill limiting lobbyist gifts to lawmakers. It gave initial approval Tuesday to a bill loosening regulations on hair braiders, but not without Democratic Rep. Michael Butler taking a rhetorical jab during debate by alluding to the governor's affair with a hairdresser.

The Senate confirmed 25 of Greitens' appointees to various boards and commissions Tuesday. A Senate panel also went forward with a hearing on a pair of tax-cut proposals, even as Greitens canceled plans Tuesday for a tour outlining his own tax reform proposals.

Meanwhile, suburban St. Louis attorney Al Watkins provided the AP with an audio recording of a fact-finding call from Lucinda Luetkemeyer, general counsel in the governor's office, that Watkins received about eight hours before the KMOV story.

Watkins, the attorney for the ex-husband of the woman involved in the affair, questioned the appropriateness of an attorney on the state payroll calling him about matters Greitens himself has described as private and personal.

"She was clearly calling me trying to facilitate damage control," Watkins said of Luetkemeyer. "If it's a private and personal matter, why is your counsel calling?"

Watkins said he turned over several hours of new audio recordings between the woman and her ex-husband to Gardner's office. He declined to discuss what was on the recordings but called it "graphic."

Watkins said those tapes also were provided to the FBI. The FBI has not confirmed if a federal investigation is underway.

Luetkemeyer in an email statement said that her office had heard Watkins was "shopping around" a story about Greitens but that she didn't know whether the story involved the governor's personal life or pertained to his official duties.

Luetkemeyer said she left her office to call Watkins and used her personal cellphone.

"Following the call, I referred the matter to the Governor's personal counsel, and advised our official press office that further comment related to this issue should be handled by the Governor's personal counsel," Luetkemeyer said in her email.

Greitens is paying his own legal fees, Bennett said.