The woman spoke to The Post after the lewd photo was published Tuesday by an anonymous Twitter account. She shared a secretly recorded phone conversation she had with Barton in 2015 in which he warned her against using the explicit materials "in a way that would negatively affect my career."
The woman described encounters and contact spanning a five-year period that began online after she posted a message on Barton's Facebook page in 2011, leading to the sexually explicit exchanges and ultimately a pair of physical sexual encounters in Washington and Texas. Over time, she said, she became aware of and corresponded with multiple other women who engaged in relationships with Barton, who represents a suburban Dallas district and is one of the most senior Republicans in the House.
The woman, who is not married, spoke on the condition of anonymity to protect her privacy.
In the 2015 phone call, Barton confronted the woman over her communications with the other women, including her decision to share explicit materials he had sent. In that context, he mentioned the Capitol Police, a comment the woman interpreted as an attempt to intimidate her.
"I want your word that this ends," he said, according to the recording, adding: "I will be completely straight with you. I am ready if I have to, I don't want to, but I should take all this crap to the Capitol Hill Police and have them launch an investigation. And if I do that, that hurts me potentially big time."
"Why would you even say that to me?" the woman responded. "The Capitol Hill police? And what would you tell them, sir?"
Said Barton: "I would tell them that I had a three-year undercover relationship with you over the Internet that was heavily sexual and that I had met you twice while married and had sex with you on two different occasions and that I exchanged inappropriate photographs and videos with you that I wouldn't like to be seen made public, that you still apparently had all of those and were in position to use them in a way that would negatively affect my career. That's the truth."
In a statement late Wednesday, Barton said a transcript of the recording provided by The Post may be "evidence" of a "potential crime against me."
He said that he received word Wednesday that the Capitol Police are opening an inquiry. While there is no federal law prohibiting the disclosure of intimate photos of adults without consent, the Dallas Morning News on Wednesday reported that the Twitter photo of Barton could violate a 2015 Texas law banning so-called "revenge porn," which is the portrayal of another person's intimate body parts and distributing the images without consent.
"This woman admitted that we had a consensual relationship," Barton said. "When I ended that relationship, she threatened to publicly share my private photographs and intimate correspondence in retaliation. As the transcript reflects, I offered to take the matter to the Capitol Hill Police to open an investigation. Today, the Capitol Police reached out to me and offered to launch an investigation and I have accepted. Because of the pending investigation, we will have no further comment."
The woman said she never had any intention to use the materials to retaliate against Barton.
A request for comment from the Capitol Police was not immediately returned late Wednesday.
Earlier Wednesday, Barton acknowledged "sexual relationships with other mature adult women" that he said took place while he was "separated from my second wife, before the divorce."
"Each was consensual," he said in a statement. "Those relationships have ended. I am sorry I did not use better judgment during those days. I am sorry that I let my constituents down."
Barton, 68, is the fifth-longest serving Republican in the House, now in his 17th term. He is a former chairman of the House Energy and Commerce Committee and now serves as vice chairman of the panel.
The Texas native has built a reputation on Capitol Hill as a fierce advocate for the oil and gas industry and a reliable vote for conservative legislation. A member of the Freedom Caucus, Barton regularly receives top scores from socially conservative groups such as the Family Research Council that analyze members' stances on positions such as abortion and gay rights.
But he is not known as an outspoken culture warrior. In 1998, amid the scandal over President Bill Clinton's affair with a White House intern, Barton was quoted in the Los Angeles Times saying, "I personally don't care a fig about what he does in his bedroom with his wife or any other sexual partners he may have, but I do care if he lies under oath."
Barton was still married to his second wife when his relationship with the woman began. His wife filed for divorce in April 2014, according to court records; the divorce was made final in February 2015. A spokeswoman for Barton did not respond to a question about when his separation began.
Besides the recording of the phone call, the woman shared text and social media messages she exchanged with Barton, as well as a 53-second cellphone video Barton recorded of himself while masturbating. The conspiracy theory website Infowars obtained a copy of the video and published it Wednesday night, though the video appeared to have been removed from the site later.
The lewd Twitter photo that Barton acknowledged on Wednesday appears to have been captured from that video. The woman said she did not post the image herself. She shared phone numbers for Barton that match his personal and government-issued cellphones. Barton was not abusive or coercive in his interactions, the woman said, but said she felt he was "manipulative and dishonest and misleading" in his dealings with her and other women.
"It's not normal for a member of Congress who runs on a GOP platform of family values and conservatism to be scouring the Internet looking for a new sexual liaison," she said, explaining her motive for coming forward.
The woman said Barton first reached out to her in 2011 after she posted a comment about politics on his Facebook page. As the two struck up a friendship, they would exchange messages for hours, including when he was on the House floor or in committee meetings, she said.
Soon, Barton began flirting, making suggestive comments and sending explicit messages, she said. She described feeling uncomfortable with his advances at first.
"He says to me, 'Do you want me to send you a picture of myself?' I said, 'Oh no, no. Please do not do that.' It kind of started there," she said.
In the spring of 2012, the woman flew to Washington, where he gave her a tour of the Capitol building, she said. The two slept together during that visit, and he reimbursed her in cash for her flight, she said.
In 2014, she visited him in Texas, where the two slept together for the second and final time, she said. He again paid for her travel, she said. "I was in it for the politics connection," the woman said of their relationship."I was kind of unwittingly drawn into it with him because of just the amazement of having a connection to a congressman," she said.
Alice Crites, Julie Tate and Michelle Ye Hee Lee contributed to this report.