The prospects of any one of Virginia’s top three leaders willingly resigning seemed to recede as the weekend wore on. Mr. Fairfax, who has denied the allegations and described the sexual encounters at the center of the claims as “consensual,” released a statement on Saturday night calling for an investigation and citing the need for “due process.”

And on Sunday morning, the governor, Ralph Northam, remained firm in his intention to stay in office and stopped short of calling for the resignations of either of his fellow scandal-plagued Democratic leaders.

In an interview with “CBS This Morning,” Mr. Northam said he was “not going anywhere” and instead would work as governor to “take action with policy to address” inequities in Virginia.

Asked about his two besieged colleagues — Mr. Fairfax and Mark R. Herring, the attorney general, who admitted to wearing blackface as a college student in the 1980s — Mr. Northam said that they “have all grown” over the last week, and that the decisions on whether to resign would have to be made by the men themselves.

The governor endorsed Mr. Fairfax’s proposal, made in a statement, to have the F.B.I. investigate the claims of sexual assault. “I really think where we are now, we need to get to the truth,” he said.

In the interview, he also said he was dedicated to continuing the work of racial progress, pointing out that the state is 400 years from the moment “the first indentured servants from Africa” landed in Virginia.

At that point the interviewer, Gayle King, chimed in: “Also known as slavery.”

It has been more than a week since a photograph showing men in blackface and a Ku Klux Klan outfit on Mr. Northam’s medical school yearbook page came to light. Nearly every day since has provided an unforeseen twist.