RICHMOND — House Republicans have renewed their call for legislative hearings into two sexual assault allegations against Lt. Gov. Justin Fairfax (D), a move that could put Democrats on the spot in the Me Too era and, perhaps, deflect attention from an upcoming special session on gun control.

In a letter sent to the House’s Democratic leader on Monday, Del. Rob Bell (R-Albemarle) said the hearings could take place as early as next month, when legislators gather July 9 for the special session Gov. Ralph Northam (D) called after a mass shooting in Virginia Beach.

“As you know, both women have stated that they will only participate in legislative hearings if the hearings are public and both Republicans and Democrats participate,” Bell,chair of the Courts of Justice Committee, wrote to House Minority Leader Eileen Filler-Corn (D-Fairfax). “I wish to renew my offer for truly bipartisan hearings.”

Filler-Corn rejected the proposal in a reply Tuesday, saying that she wanted to hear from Fairfax’s accusers but feared that Republicans would run the hearing as a “political exercise.”

“We will not participate in House Republicans’ political games, nor will we turn such serious allegations into a partisan sideshow,” Filler-Corn wrote.

Republicans, who will try to defend a narrow House majority in November elections, have been pressing for hearings since early this year, when two women came forward to accuse Fairfax of sexually assaulting them in the early 2000s.

Fairfax has denied the allegations and said the encounters were consensual.

Vanessa Tyson, a college professor in California, accused Fairfax of forcing her to perform oral sex after they met at the 2004 Democratic National Convention in Boston. Meredith Watson said Fairfax sexually assaulted her in 2000, when they were undergraduates at Duke University.

Tyson’s attorney, Debra Katz, did not immediately respond to a request for comment.

Watson’s attorney, Nancy Erika Smith, said in an email: “No comment . . . yet.”

Lauren Burke, a spokeswoman for Fairfax, reiterated the lieutenant governor’s recent call for prosecutors to investigate the allegations and accused Bell and House Speaker Kirk Cox (R-Colonial Heights) of playing politics and trying to distract from the issue of how to reduce gun violence.

“A Republican show trial during an election year is not an investigation that will reveal the truth,” Burke said.

Last week, Fairfax’s lawyer wrote to prosecutors in the two states where the alleged assaults were said to have taken place, asking that they open criminal probes into the women’s claims. Fairfax offered to testify under oath to the prosecutors in Boston and Durham, N.C.

Lawyers for the two women dismissed Fairfax’s offer — one called it a “stunt” — and repeated their clients’ desire to testify before lawmakers instead. That gave Bell an opening to revive their push for hearings, something House Democrats rebuffed during this year’s General Assembly session.

Fairfax’s scandal has put Democrats in an awkward position, particularly in a political moment when the party nationally has preached zero tolerance for sexual harassment and assault. While Virginia Democrats have called for Fairfax’s resignation, they also have said legislative hearings would be a political circus, with none of the established rules for evidence and procedure that would govern a criminal proceeding.

All 100 seats in the House and all 40 in the Senate are on the ballot in the fall, with Republicans holding narrow majorities in each chamber. Republicans hope to capitalize on scandals plaguing the state’s three top Democrats — separate from the allegations against Fairfax, both Northam and Attorney General Mark R. Herring admitted earlier this year that they dressed in blackface decades ago to imitate African American singers — as they try to keep control of the legislature.