The fallout over Missouri Gov. Eric Greitens’ admitted affair and allegations of blackmail was swift, with the local prosecutor heeding Thursday's calls from Republicans and Democrats for an investigation, and some Democrats suggesting the governor should resign.

On KCUR’s Up to Date talk show, Democratic Reps. Jon Carpenter and Judy Morgan, both of Kansas City, said Greitens should resign, calling it the “right thing for Missouri.”

“To me it’s way beyond the pale. I don’t see how we can move forward as a state with Eric Greitens as governor,” Carpenter said.

Earlier, Senate Democratic leaders Gina Walsh of Bellefontaine Neighbors, and Kiki Curls of Kansas City issued a statement that said these were “very serious allegations” and that “violence and threats against women are never acceptable.”

“Allegations of extortion, coercion or threats of violence must be investigated by the proper authorities,” they wrote.

Republican Sens. Doug Libla of Poplar Bluff and Gary Romine of Farmington both asked Attorney General Josh Hawley to investigate the allegations, which come as the 2018 legislative session is getting underway. (Already, Hawley is investigating Greitens' and his staff's use of a secretive app to find out whether official public business was conducted and then deleted.)

“The only way we can remove this cloud is to get all the facts,” Romine was quoted by the Kansas City Star. “We need this to move as quickly as possible. If it exonerates him, we can move on. If it doesn’t, he needs to resign or face impeachment.”

But Hawley doesn't have the jurisdiction to do so, only the prosecutor in the "place where the conduct occurred," spokeswoman Loree Anne Paradise told KCUR in an email Thursday. That person is St. Louis Circuit Attorney Kim Gardner, who said in a statement announcing her investigation that it's essential for residents of the city and state to "have confidence in their leaders."

Greitens, through his lawyer, has denied the allegations that he took a photo of the woman he had an affair with while she was blindfolded and naked and threatened her not to speak of the relationship. The lawyer, James Bennett, also said Thursday that the story is a "political hit piece."

Statement from James F. Bennett, our attorney pic.twitter.com/l4VreENKRT — Eric Greitens (@EricGreitens) January 11, 2018

In a statement released through Twitter and Facebook on Wednesday night, Greitens and his wife, Sheena, said the affair, which happened in 2015 before he ran for governor, was a “deeply personal mistake” and that the couple had worked through it.

Overshadowing the governor’s State of the State address, the affair, Greitens’ admission and the allegations of blackmail were revealed by St. Louis TV station KMOV. The report is based on a secretly recorded conversation between the unidentified woman, who allegedly worked at a salon Greitens went to in St. Louis, and her now ex-husband. (It is legal in Missouri to tape a conversation without both parties’ consent.)

KCUR has not been able to independently confirm the report. The woman has not publicly commented, and the ex-husband provided the tape to the TV station on condition of anonymity. It isn’t clear whether the woman knew her ex-husband was in communication with media outlets about the story.

KCUR contacted several Republican lawmakers for comment, but they either declined or reporters had to leave messages. GOP Sen. Caleb Rowden of Columbia said on Twitter he'd like to see an investigation by law enforcement.

My statement re: the recent allegations against Governor Eric Greitens. #MOLeg pic.twitter.com/PJYuSHjBn7 — Caleb Rowden (@calebrowden) January 11, 2018

"It’s a really sad state of affairs in our politics and other parts of our society when things like this keep happening,” Democratic Rep. Judy Morgan of Kansas City told KCUR about the alleged blackmail coming at a time of increased awareness and revelations of sexual impropriety and assault in several fields.

She and Democratic Rep. DaRon McGee of Kansas City said they’re worried about what effect the affair and the allegations will have when it comes to the perception of the state. McGee said: “we have some tough issues we’re dealing with in this legislative session and no one is talking about his State of the State address that did not focus on education, did not address health care. … This is a definite distraction.”

KCUR's Erica Hunzinger contributed to this report.

KCUR's Brian Ellison is the host of Statehouse Blend Missouri and contributes to coverage of Missouri government. He can be reached by email or followed on Twitter, @ptsbrian.