Mourdock said some people have interpreted his remarks at a debate on Tuesday night (local time) as condoning rape. Mourdock said he abhors rape and violence against women.
"I apologize that they came away, and I have certainly been humbled by the fact that so many people think that somehow was an interpretation," Mourdock said at a press conference on Wednesday.
Mourdock made the controversial comments during a campaign debate with Democratic Representative Joe Donnelly and Libertarian Andrew Horning.
While explaining his position that the only exception to a ban on abortion should be for the life of a mother, Mourdock said: " I struggled with it myself for a long time, but I came to realize that life is that gift from God, and I think even when life begins in that horrible situation of rape, that it is something God intended to happen."
The Mourdock incident was the second time during the 2012 election campaign that a conservative Republican candidate for the U.S. Senate made controversial remarks about rape.
Missouri candidate Todd Akin said in August that women have natural defences against pregnancy from "legitimate rape." Republicans disavowed Akin's comment and he has trailed Democratic Senator Claire McCaskill in most polls since then.
Some Republicans distanced themselves from Mourdock's comments on Wednesday and Democrats pounced on the remarks, which threatened to put at risk in November a U.S. Senate seat held by Republicans.
President Barack Obama's campaign spokeswoman Jen Psaki said the president believed Mourdock's comment was "outrageous and demeaning to women," and it was "perplexing" that Romney had not demanded a television ad he filmed on behalf of Mourdock be scrapped.
"This is a reminder that a Republican Congress working with a Republican president, Mitt Romney, would feel that women should not be able to make choices about their own healthcare," Psaki told reporters tra veling with the president on Air Force One to the swing state of Iowa.
Romney's campaign distanced him from the remark, saying the candidate disagreed with it and it did not reflect his views.
Earlier in the week, the Mourdock campaign issued a television and radio ad featuring Romney's endorsement of the Indiana Republican, saying that Mourdock's vote in the Senate could be crucial to repealing Obama's health reform law.
Mourdock defeated longtime Senator Richard Lugar in the Republican primary, dividing the Republican Party. He has since struggled to establish a significant lead in polls against Donnelly.
Loss of what was once considered a safe Republican seat in Indiana would be a severe blow to Republican hopes of taking control of the U.S. Senate.
Mourdock said on Wednesday that his comments had been "twisted" by some people.
"I absolutely abhor violence. I abhor any kind of sexual violence," he said. "I am absolutely confident that the God I worship abhors violence."
