Kansas Attorney General Phill Kline has demanded that clinics hand over records of nearly 90 women who had abortions.
Kansas Attorney General Phill Kline says he has a duty to children
He is seeking the women's names, sexual history and medical details, saying he wants to investigate possible child rape or illegal abortions.
But the clinics involved accuse Mr Kline, an abortion opponent, of trying to launch a "secret inquisition".
They say he is "fishing" rather than investigating a specific crime and want the state Supreme Court to intervene.
Mr Kline began the inquiry in October but it only became public when the clinics filed an appeal against a court order to hand over the records.
In the appeal to the Kansas Supreme Court the two clinics, which have not been named, said the records contained "the most intensely private information a woman can disclose", adding that much of the information would be irrelevant in any criminal investigation.
If the records were disclosed, the claim continued, "the logical and natural progression of this action could well be a knock on the door of a woman... by agents of the attorney general who seek to inquire into her personal, medical, sexual, or legal history".
Mr Kline told reporters at a brief news conference that he requested the information to uncover evidence that could be used in investigations that could include child rape.
"When a 10, 11 or 12-year-old is pregnant, under Kansas law that child has been raped," he said.
"I have the duty to investigate and prosecute child rape in order to protect Kansas children."
No hearing has yet been scheduled for the appeal.
Kansas restricts abortions after 22 weeks of pregnancy, except where a continuation could seriously harm the mother's health,
But the New York Times reported that the state has become a magnet for late-term abortions because of a doctor in Wichita, George Tiller, who performs hundreds of the procedures each year.
Dr Tiller's lawyer would not say if his clinic was one of the two targeted by Mr Kline, but said every instance of suspected child abuse was reported.
Correspondents say the case will be watched for its broader implications and privacy experts say they are concerned.
Pam Dixon, of World Privacy Forum, told the Kansas City Star newspaper: "This is not a slippery slope we're going down. It's the opening of a Pandora's box."