Greitens responded on Twitter, saying, quote, "I will not be resigning the governor's office".
Hawley announced an investigation into Greitens and his charity, The Mission Continues, in March.
Greitens' attorneys also asked the judge to appoint a special prosecutor, independent of Hawley's office, for purposes of conducting any such investigation.
Hawley's investigation alleges Greitens used the charity donor list to solicit campaign funds.
Hawley stated that St. Louis attorneys are now investigating all the material that has been sent over to them.
The leader of the Missouri House Democrats is renewing her call for Gov. Eric Greitens to step down or be impeached in response to an announcement from the state attorney general that evidence shows Greitens' use of a charity donor list potentially broke the law.More news: Saudi Arabia Looking for Crude Oil at $100 bbl
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They also said that the woman who had an affair with Greitens had been "wholly consistent in the core of her testimony", despite defense challenges to her story. Questions have been raised about his ties to the charity since at least October 2016, when The Associated Press reported that he had raised almost $2 million for his campaign from donors who also gave significant amounts to The Mission Continues.
Attorney General Josh Hawley announced Tuesday that his investigation into a veterans charity founded by Greitens found evidence that Greitens may have committed a felony in his use of its donor list for political purposes.
August 2007: Greitens, a former Navy SEAL officer, founds the charity The Mission Continues in St. Louis. His spokeswoman Mary Compton said in a statement that Hawley became involved after the St. Louis Post-Dispatch reported in February 2018 that it had obtained a copy of an email indicating that a Greitens employee who previously worked at The Mission Continues had shared the donor list with Laub and Michael Hafner, who had been working for Greitens' gubernatorial exploratory committee, in January 2015. "In our view, the time has come for the governor to resign", House Speaker Todd Richardson said in a joint statement with House Speaker Pro Tem Elijah Haahr and House Majority Floor Leader Rob Vescovo.
Before he was governor, Greitens founded The Mission Continues, a charity that helps military veterans returning from war.
A growing number of Missouri elected officials have called on Greitens to step down over allegations of unwanted sexual aggression against a woman with whom he has said he had a consensual extramarital affair in 2015.
August 2016: Greitens wins a tough, four-person race for the Republican nomination for governor.