Todd Akin, who is also running as Republican candidate for the Senate, made the comments in a TV interview to explain his strict views on abortion.
He later said he had “misspoken” but his Democratic rival said the comments were “beyond comprehension”.
Republican presidential candidate Mitt Romney said he disagreed with the view.
During the interview for KTVI-TV, Todd Akin was asked about his no-exceptions view on abortion, a highly charged issue in the US, and on whether he would like abortion to be banned even if the pregnancy was the result of rape.
He replied: “It seems to me, from what I understand from doctors, that is really rare.
“If it’s a legitimate rape, the female body has ways to try to shut that whole thing down.
“But let’s assume that maybe that didn’t work or something: I think there should be some punishment, but the punishment ought to be of the rapist, and not attacking the child.”
The interview has sparked a furious reaction in the US, with critics attacking both Todd Akin’s scientific view and his reference to “legitimate rape”.
Democrat Senator Claire McCaskill said it was “beyond comprehension that someone can be so ignorant about the emotional and physical trauma brought on by rape”.
“The ideas that Todd Akin has expressed about the serious crime of rape and the impact on its victims are offensive.”
Claire McCaskill, who is trailing Todd Akin in opinion polls for the Missouri seat, said on Twitter that as a former prosecutor she had personally handled hundreds of rape cases.
On blogs and Twitter, users have also poured scorn on his biological view, and expressed concern that he is a member of the House Committee on Science.
Terry O’Neill, president of the National Organization for Women, told AP radio that the comments were “flat-out astonishing” and that such language was “intended to shame women”.
A spokesman for Mitt Romney said that both the candidate and his running mate, Paul Ryan, disagreed with Todd Akin, and stressed that “a Romney-Ryan administration would not oppose abortion in instances of rape”.
Todd Akin later issued a statement saying he had “misspoken” in his “off the cuff” remarks, though did not specify on which points.
He said the interview “does not reflect the deep empathy I hold for the thousands of women who are raped and abused every year”.
Todd Akin also reconfirmed that he “believes deeply in the protection of all life and I do not believe that harming another innocent victim is the right course of action”.
The six-term congressman for Missouri is a long-time vocal opponent of relaxing abortion laws.
In 2011, he co-sponsored a controversial bill that would have limited the government help available to women seeking abortions in the case of rape to cases of “forcible rape”.
After a public outcry, the House Republican party was made to change this language.
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