The St. Louis circuit attorney on Thursday opened an investigation into claims that Gov. Eric Greitens of Missouri, a former Navy Seal regarded as a Republican rising star, threatened a woman with whom he had an extramarital affair shortly before he was elected governor.

Mr. Greitens had acknowledged the night before that he had an affair in 2015, but denied he had threatened the woman with whom he had the relationship.

“The serious allegations against Missouri Governor Eric Greitens are very troubling,” said Kimberly Gardner, the city prosecutor and a Democrat, in a statement, adding: “It is essential for residents of the City of St. Louis and our state to have confidence in their leaders. They must know that the Office of the Circuit Attorney will hold public officials accountable in the same manner as any other resident of our city.”

The accusations were relayed by the woman’s ex-husband, but she has not commented.

Mr. Greitens and his wife, Sheena, released a joint statement after a number of inquiries from the news media about the relationship late Wednesday night, shortly after the governor’s State of the State address, in which the couple revealed that there “was a time when he was unfaithful in our marriage.”