Sen. Maria Chapelle-Nadal, a Democrat, wrote on her personal Facebook page Thursday, "I hope Trump is assassinated!" She later deleted the post.
Chapelle-Nadal has balked at calls for her resignation.
"I am not resigning," she tweeted Thursday. "When POC [people of color] are respected by this WH & they are willing to do real work, I'll sit down with them. People are traumatized!"
So Gov. Greitens and Lt. Gov. Mike Parson, both Republicans, on Friday called for Chapelle-Nadal's colleagues to oust her.
"If she will not resign, the Senate can vote to remove her. I believe they should," Greitens tweeted.
The Republican governor previously tweeted, "Senator Chappelle-Nadal said she hopes the President is killed. Republicans and Democrats have called on her to resign ... Her response: 'Hell no.' Last night, in an interview, she refused to apologize -— twice."
Chappelle-Nadal told The Associated Press on Friday that she met on Thursday with the U.S. Secret Service as part of its investigation into her remarks.
"I let them know that I had no intentions of hurting anyone or trying to get other people to hurt anyone at all," she said.
And in an interview with the St. Louis Post-Dispatch, she said, "I didn’t mean what I put up. Absolutely not. It was in response to the concerns that I am hearing from residents of St. Louis.”
Chappelle-Nadal made the remark in response to a post that suggested Vice President Mike Pence would try to have Trump removed from office. Chappelle-Nadal said she made comment out of frustration with the Trump's response to last weekend's white nationalist rally in Charlottesville, Virginia.
Parson said he will ask senators to remove Chappelle-Nadal from office if she does not resign by the time lawmakers convene Sept. 13 to consider veto overrides. Parson is the presiding officer of the Senate, though he can only vote to break ties and cannot sponsor legislation or make motions for votes.
"She is no longer fit to serve our state," Parson said at a Capitol press conference Friday.