The heightened scrutiny of sexual impropriety on Capitol Hill has swept up a senior House Republican who apologized Wednesday for a sexually explicit photograph that wound up on the internet and raised the possibility that he had been the victim of a crime.

Representative Joe Barton of Texas, who was once the chairman of the House Energy and Commerce Committee and is now its vice chairman, said that he was reconsidering his political future after the photograph appeared on an anonymous Twitter account.

Mr. Barton, who has hired a crisis communications firm, made clear he was ready for a fight. In a statement Wednesday night, he said that he had suffered “a potential crime.” A Texas law, the so-called revenge pornography law, makes it a misdemeanor to intentionally publicize images or videos of someone’s genitals or sexual activity without consent.

Hours after his initial apology, The Washington Post reported that Mr. Barton, 68, had threatened in 2015 to report to the Capitol Police a woman with whom he had shared explicit photographs, videos and messages if she exposed him.

The woman, who spoke anonymously, shared with The Post a recorded phone conversation in which the congressman confronted her about communications she had with other women connected to Mr. Barton, including sexually explicit material he had shared with her.

Mr. Barton did not dispute the woman’s account. But in his statement, he said that she “threatened to publicly share my private photographs and intimate correspondence in retaliation” when he ended their relationship.

“Today, the Capitol Police reached out to me and offered to launch an investigation and I have accepted,” he said. “Because of the pending investigation, we will have no further comment.”

A spokeswoman for the Capitol Police did not immediately reply to a request for comment.

In his earlier statement, Mr. Barton had said that while separated from his wife, he had “sexual relationships with other mature adult women.”

“Each was consensual. Those relationships have ended,” he said. “I am sorry I did not use better judgment during those days. I am sorry that I let my constituents down.”

The photograph of a naked Mr. Barton, with his genitals obscured before it was posted, set off waves of speculation in Texas and Washington, where sexual harassment charges are roiling Capitol Hill. The tweets, which appeared Monday, included an image of a sexually explicit text message, ostensibly sent by Mr. Barton, along with a cryptic reference to harassment.

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