In a statement, Mr. Fairfax’s spokeswoman did not indicate whether he would testify but accused Republicans of “engaging in political theater” and said they were seeking partisan gain from the accusations.

“House Republicans want to pursue this historically unprecedented course of action because the accused is a popularly elected Democrat,” said Lauren Burke, Mr. Fairfax’s spokeswoman.

The sexual assault claims, Ms. Burke said, should be taken up by “law enforcement professionals.”

House Republicans framed their decision to move forward with the hearings as a response to the requests of the two accusers, who have been urging the Legislature to investigate and have repeatedly stated their willingness to testify. But the inquiry could also make the election-year quandary Virginia Democrats find themselves in even more painful.

The specter of public hearings into the allegations against Mr. Fairfax, who is black, would not only revive a scandal that had started to quiet, it would also serve as a reminder that Gov. Ralph Northam and Attorney General Mark Herring, who are white, have refused to resign after admitting they wore blackface in their youth. All 140 seats in the Virginia General Assembly are on the ballot in November and Republicans are clinging to narrow majorities in both chambers.

[Read more about how Mr. Northam is trying to repair his relationship with black Virginians.]

House Republicans and Democrats had met earlier in the week to discuss crafting a bipartisan response, but by Thursday were criticizing one another over how to deal with the claims against Mr. Fairfax.

The Republicans had sought to create a 10-person investigative panel, equally divided between parties, to examine Ms. Watson’s claim that Mr. Fairfax raped her in 2000, when they were Duke University students, and Dr. Tyson’s accusation that he sexually assaulted her during the 2004 Democratic convention in Boston.

But Democrats were uneasy about creating a forum they said would politicize the accusations and indicated they would prefer that law enforcement handle the matter.