The Washington Post reported the threat Wednesday after Barton, a North Texas Republican, apologized for a nude photo of him that circulated on social media.
The photo of Barton appeared on an anonymous Twitter account. It was not immediately known who posted the photo or when it was taken.
Barton issued a statement saying that while separated from his second wife, prior to their divorce in 2015, he had sexual relationships “with other mature adult women.” The 68-year-old Republican said each relationship was consensual and has since ended.
“I am sorry I did not use better judgment during those days. I am sorry that I let my constituents down,” said Barton, the longest-serving member of Congress from Texas.
However, a woman whom the Post did not identify told the newspaper of Barton’s threat over the sexually explicit photographs, videos and messages he had sent to her. The woman described sexual encounters and contact extending over five years, beginning with her posting of a message on Barton’s Facebook page in 2011.
She also shared with the Post a secretly recorded telephone conversation with Barton in 2015 in which he warned her against using the material “in a way that would negatively affect my career.”
The Post reported the woman, who is not married, spoke on the condition of anonymity to protect her privacy.
A message left by The Associated Press at Barton’s district office in Arlington, Texas, was not returned. The voicemail for his office in Washington was full.
In a statement to the Post, Barton said a transcript of the telephone conversation provided by the newspaper may be “evidence” of a “potential crime against me.” He also said that Capitol Police had informed him Wednesday that they were opening an inquiry.
Capitol Police did not respond to a request by the AP for comment late Wednesday.
Earlier in the day, Barton’s spokeswoman told The Dallas Morning News that the congressman has no plans to step down.
Barton, a member of the conservative House Freedom Caucus, announced his re-election bid this month. His district includes several counties in the Dallas-Fort Worth area.
Barton was a consultant in the oil and gas industry before he joined the U.S. House in 1985.
He is currently the vice chairman of the powerful House Energy and Commerce committee. He was the committee’s chairman from 2004 to 2007.
Barton has also been the longtime manager of the GOP congressional baseball team. He was taking part in a team practice in June when a gunman opened fire, injuring another congressman and others.