Trent Franks is accused of offering a former aide $5m to act as a surrogate mother
The announcement came after a congressional panel said it was opening an inquiry into sexual harassment allegations against Mr Franks.
The lawmaker acknowledged discussing surrogacy with two female aides when he and his wife were facing infertility.
He is the third member of Congress to resign in three days.
The Associated Press reports one of Mr Franks' former aides accuses him of offering her $5m (£3.7m) to act as a surrogate mother, repeatedly pressing her to carry his child.
Comment: That's a novel way to proposition a woman. Excuse us if we are somewhat skeptical that Franks' motive was merely to find a way to produce an heir to his throne. First of all, he already has two children. Second, those two children were born by a surrogate mother after in vitro fertilization with a donor egg, which means Trents' wife can't bear children. Since the couple have already availed themselves of a surrogate mother from a known surrogate agency run by a Dr. Wertman, why would Trent not simply use the same service again? The only difference between doing that and propositioning his aides is that he gets to have sex with them.
She told the news agency that another female staff member had also been approached by Mr Franks about surrogacy.
One of the aides reportedly said Mr Franks retaliated against her after she turned down his alleged surrogacy requests by ignoring her and withholding assignments.
A spokesman for the eight-term congressman - who has a net worth of $33m - would not comment on whether he had offered aides money to act as surrogates.
Mr Franks said on Thursday his resignation would take effect next month.
But on Friday he said he had decided to quit immediately after his wife was admitted to a Washington hospital "due to an ongoing ailment".
Comment: The above suggests that Trents' wife was unaware of his indecent proposal and understood it for what it was.
In a statement on Thursday, the 60-year-old Republican acknowledged "my discussion of surrogacy with two previous female subordinates, making each feel uncomfortable.
"I deeply regret that my discussion of this option and process in the workplace caused distress."
Mr Franks said he and his wife, Josephine, had used a surrogate to carry their two twins.
He stood down as the House of Representatives ethics committee opened an inquiry against him into a matter that "constitutes sexual harassment and/or retaliation for opposing sexual harassment".
Republican Speaker of the House Paul Ryan said he had advised the congressman to stand down.
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