The House Ethics Committee later announced that is had opened an investigation of allegations Mr. Franks "engaged in conducted that constitutes sexual harassment and/or retaliation for opposing sexual harassment".
Andrea Lafferty, president of the Traditional Values Coalition, told CNN that the accuser - a former aide whom she did not name - said that she was asked to look over a contract to carry Franks' child.
He was expected to make a statement Thursday; the aide was not authorized to discuss the matter before Franks' announcement.
Franks says he deeply regrets "that my discussion of this option and process in the workplace caused distress".
In his statement, Franks said he never "physically intimidated, coerced, or had, or attempted to have, any sexual contact with any member of my congressional staff".
Franks says he had become familiar with the surrogacy process in recent years, and "became insensitive as to how the discussion of such an intensely personal topic might affect others".
House Speaker Paul D. Ryan, Wisconsin Republican, said the companies against Mr. Franks were "credible" and that he had personally urged Mr. Franks to resign.
Franks said he will step down effective January 31. He said he discussed these issues with two female subordinates. After having twins with a surrogate, the couple sought additional children, he said.
Ryan says he presented the allegations to Franks, which he did not deny, and told Franks he would refer the allegations to the House Ethics Committee. Al Franken, who also announced his resignation on Thursday.
"We're trying to get that done before the holidays, over the next few weeks", Alderman said.
Franks represents Arizona's 8th district and first entered Congress in 2002. He continued as chairman of a House Judiciary subcommittee and as a member of the House Armed Services Committee. It was not immediately clear why Mr. Franks was resigning.
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