WASHINGTON — The heightened scrutiny of sexual impropriety on Capitol Hill has swept up a senior House Republican who apologized Wednesday for a sexually explicit photo 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.

Just hours after the apology, TheWashington 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.

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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. In a statement Wednesday night, he said that she “threatened to publicly share my private photographs and intimate correspondence in retaliation” when he ended their relationship.

“As the transcript reflects, I offered to take the matter to the Capitol Hill Police to open an investigation,” he said. “Today, the Capitol Police reached out to me and offered to launch an investigation and I have accepted.”

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 photo of a naked Mr. Barton, with his private parts 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 on Monday, included an image of a sexually explicit text message, ostensibly sent by Mr. Barton, along with a cryptic reference to harassment.

It was not clear why the photo was posted. Lawmakers called and texted one another Tuesday night and Wednesday morning trying to discern whether the photo was authentic, but received no guidance from the party’s leadership or Mr. Barton.

AshLee Strong, a spokeswoman for Speaker Paul D. Ryan of Wisconsin, said Mr. Ryan had spoken to Mr. Barton on the matter but would “keep those conversations between the two of them.”

Mr. Barton is the longest-serving member of the Texas congressional delegation and was the Energy and Commerce Committee chairman when President George W. Bush was in the White House.

He had lowered his sights more recently, telling associates that he hoped to claim the investigatory subcommittee of the Energy and Commerce panel. That subcommittee chairmanship is currently vacant because its most recent chairman, Representative Tim Murphy of Pennsylvania, resigned last month after it was revealed that he had encouraged his mistress to seek an abortion.

Unlike other veteran lawmakers who have retired after their time atop influential committees has come to an end, Mr. Barton had shown no interest in leaving Congress.

“I’m the odd duck who didn’t quit,” he joked to The Dallas Morning News in an interview this month.

His personal life has been more turbulent than his political career. He divorced his first wife in 1993 and his second wife two years ago.

Mr. Barton has young children from his second marriage, and one of them, his 10-year-old son, was at the congressional baseball practice earlier this year when a man sprayed the field with bullets, gravely injuring Representative Steve Scalise. Mr. Barton is the longtime coach of the Republican baseball team.

Democrats were not planning to aggressively contest Mr. Barton’s conservative-leaning seat: His best-funded challenger, Jana Lynne Sanchez, had only $16,440 on hand as of the start of October.