“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.

In addition to the recorded phone conversation, The Post reported that the woman had shared messages she exchanged with the congressman and a cellphone video of the congressman masturbating. The Post, which reviewed the video, said the photograph posted on Tuesday appeared to be a still shot from the video.

It was not clear why the photograph was posted. The woman who spoke with The Post said she had not put the image on Twitter herself. Lawmakers called and texted one another Tuesday night and Wednesday morning trying to discern whether the photograph was authentic, but received no guidance from the party’s leadership or Mr. Barton.

Direct messages sent to the Twitter account that posted the image have not been returned.

AshLee Strong, a spokeswoman for Speaker Paul D. Ryan of Wisconsin, said Wednesday afternoon that 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, Republican of Pennsylvania, resigned last month after it was revealed that he had encouraged his mistress to seek an abortion.