(CNN/KMOV) -- A number of Republican state lawmakers issued blistering calls Tuesday for Gov. Eric Greitens to step down, a sign of mounting pressure on the embattled governor in the aftermath of allegations that he had blackmailed a woman he had an affair with.

The lawmakers included state Rep. Nate Walker, who was one of Greitens' earliest supporters during the contentious Republican primary, listed in January 2016 among the campaign's state leadership team.

Walker said Tuesday that Greitens' "scandal will make it impossible to lead the state going forward."

"It is my belief the governor should resign so that the state can move forward focusing on the issues that we all care about," Walker added.

Earlier in the day, state Reps. Marsha Haefner and Kathie Conway also had issued calls for the governor to step down, expressing doubts that he would be able to govern effectively in light of the controversy enveloping him.

"I find no pleasure in saying this, but I believe Gov. Greitens is no longer fit to hold Missouri's highest office," Haefner said. Greitens, she added, "no longer has the trust and support of many in the Legislature."

"We have to work as a team to accomplish what citizens expect us to do, but our leader is now ineffective," Haefner continued. "Missourians deserve better. There is too much at stake."

Conway, who had spoken with the governor in recent days and noted that she's a longtime supporter of his, said she had taken "the weekend to think, study the facts and pray about" her decision. "With that heavy heart," Conway added, "I ask the governor to consider resigning and allow the state to move forward with its work for our citizens."

Conway also invoked her experience as a former criminal investigator to warn of a potentially "long process that will be humiliating to everyone" in the coming weeks.

"There would be no privacy that can be realistically offered when the governor of a state is under investigation," Conway said. "All the while, our state will continue to be embarrassed on the national stage."

The calls for Greitens to step down came as the Missouri Legislature was set to reconvene Tuesday.

Privately, Greitens has attempted to prevent the floodgates from opening. Last week, as CNN previously reported, he phoned state Senate and House lawmakers of both parties --- apologizing for his affair, denying the allegations of blackmail and assuring them there would be no new revelations. His wife, Sheena, joined him on the line for some of those calls.

Meanwhile the governor has maintained a low public profile, abruptly postponing a statewide tour to promote a tax-cut proposal that had been slated for this week.

But in spite of his efforts, Greitens likely will not be able to shake his controversy soon. St. Louis circuit attorney Kim Gardner announced last week that she has opened a formal investigation into the governor, opening the door for new details or revelations to emerge.

Missouri Gov. Eric Greitens released a new statement about an affair he was involved in and allegations connected to that affair.

In a statement posted to Facebook, Greitens said he made a “personal mistake” and says he is sorry for the pain it caused for his family, friends and others.

He goes on to say that “much has now been written about this, and many of the assertions made have not been truthful and have proven extremely hurtful to Sheena, as well as to me.”

In a recording obtained by News 4, a woman is heard admitting to her then husband that she had a sexual encounter with Greitens in 2015, more than one year before he was elected governor.

The woman’s ex-husband alleges Greitens tried to blackmail her to keep the affair quiet.

The woman and her husband later divorced. Her attorneys have said she was recorded without her permission and is asking for privacy. She has chosen not to speak about the matter on-the-record

Greitens has admitted to the affair but has denied other allegations.

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