Democrats who hoped they had found an answer to racism charges against Virginia’s governor were stung Monday when his heir apparent, Lt. Gov. Justin Fairfax, had to fend off rape allegations.

Surrounded by reporters at the State Capitol in Richmond, Mr. Fairfax tackled the #MeToo-style allegation head-on.

Admitting to a consensual one-night stand with his accuser in 2004, the lieutenant governor said it was years later that she objected to their encounter and made him the victim of a political “smear.”

He described his accuser as a spurned lover, not a rape victim.

“Everything was 100 percent consensual. Not only that, the same person called me sometime later and wanted to meet with me, wanted to come visit me [and] wanted me to meet her mother,” said Mr. Fairfax, a Democrat.

Whether forced or consensual, Mr. Fairfax and the woman agree that the sexual encounter took place in a hotel room in Boston when both were campaign staffers at the 2004 Democratic National Convention.

Attributing sinister motivations to his accuser, Mr. Fairfax said he took biblical advice and donned “armor of God” that “allows us to deal with the devil’s schemes and tricks.”

The accusation of sexual misconduct swamped Mr. Fairfax as he waited in the wings for Gov. Ralph Northam, also a Democrat, to heed unrelenting calls to resign over a racist yearbook photo.

The lieutenant governor, who is black, was viewed as their party’s savior when the photo from Mr. Northam’s profile page in his 1984 medical school yearbook came to light Friday. The photo showed somebody in blackface standing beside another person in a Ku Klux Klan outfit, presumably Mr. Northam and a friend.

Mr. Northam apologized Friday and admitted taking part in the photo, though he did not say whether he was in blackface or the KKK robes and hood. At a bizarre press conference Saturday, he said that on closer inspection he realized that he had never participated in such a photo and had never before seen the image or the yearbook.

The governor admitted that in 1984 he put a small amount of black shoe polish on his face while dressed as Michael Jackson for a dance contest, which he won.

“The reason I used a very little bit is because, I don’t know if anybody has ever tried that, but you cannot get shoe polish off,” Mr. Northam said at the press conference.

Virginia’s Democratic elected leaders, the state Democratic Party and every Democratic presidential candidate has urged Mr. Northam to resign.

The governor met privately with top administration officials but gave no public indication that he would resign.

Virginia House Speaker Kirk Cox, a Republican, said he did not plan to impeach or otherwise force out Mr. Northam.

“I think there’s a rightful hesitation about removal from office because, obviously, you have to consider that to some degree you are overturning an election,” he said.

Still, he said the governor had lost the ability to lead the state and should resign, regardless of the veracity of the photo.

Mr. Fairfax stopped short of calling for Mr. Northam’s resignation. Being the designated successor put him in a “unique position,” he said.

“I believe the governor has to make the decision that is in the best interest of the Commonwealth of Virginia, and I know there are many others who have called on him to resign,” Mr. Fairfax said.

After the racist photo emerged, Mr. Northam’s approval rating plummeted from 48 percent to 29 percent, according to a Morning Consult poll.

Among Virginia Democrats, Mr. Northam’s approval dropped from 70 percent before the controversy to 50 percent. It fell from 42 percent to 20 percent among independents and from 31 percent to 15 percent among Republicans.

If Mr. Northam relents and steps down, he would be the first Virginia governor to not complete his term in office. Mr. Fairfax would then have a shot at leading Virginia for a record seven consecutive years in a state where the governor is limited to one four-year term.

It would be a historic opportunity for Mr. Fairfax, who at age 39 is a rising star in the Democratic Party, to leave an indelible stamp on Virginia politics and two presidential elections.

“Virginia’s ban on governors serving consecutive terms does not apply to someone who succeeds to the governor’s office midterm,” said Wake Forest University political science professor John Dinan, a top scholar of the Virginia Constitution.

He noted that prohibition has been on the books since 1830 and no Virginia governor since that time has been allowed to succeed himself in office. One governor, Mills Godwin Jr., served eight years in nonconsecutive terms, as a Democrat from 1966 to 1970 and as a Republican from 1974 to 1978.

“A resignation from Northam would open the possibility for Fairfax to serve nearly seven years as governor, if he were to run for and win in 2021, and that would be a significant length of time for a Virginia governor,” Mr. Dinan said.

That the rape allegation resurfaced now underscored the political motivation behind it, Mr. Fairfax said.

The woman made the same allegations to The Washington Post last year after Mr. Fairfax was elected lieutenant governor. He said the paper dropped the story after a lengthy investigation found it “was not credible because it was uncorroborated.”

The newspaper, however, said the woman and Mr. Fairfax told different stories about what happened in the hotel room and neither version could be corroborated.

The woman told the newspaper that what began as consensual kissing turned into him forcing her to perform oral sex.

Mr. Fairfax said the sex was consensual.

“I was 25 years old, unmarried, a campaign staffer at the time. We hit it off,” he told a throng of reporters. “She was very interested in me and so eventually at one point, we ended up going to my hotel room. This is 2004. She is very much into a consensual encounter and even admits in the story there is consensual activity going on.”

He said the accuser revived the story because of the political turmoil in Richmond. “This person then went into hiding and laid low in the weeds and then the second that this issue cropped up in Virginia with a lot of media attention, [she] crops back up with the same false allegation and uses others to get it out into the mainstream media,” he said.

The conservative news site Big League Politics first published the woman’s story based on a post on social media. The same website also first reported on Mr. Northam’s racist yearbook photo.

The newspaper did not publish the woman’s account until it appeared on the conservative news website.

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