Appearing on former presidential candidate Mike Huckabee's radio show, Akin said rape is "never legitimate."
"It's an evil act. It's committed by violent predators," Akin said. "I used the wrong words the wrong way."
Calls for Akin's exit from the race grew Monday, with at least two Republican senators - Scott Brown of Massachusetts and Ron Johnson of Wisconsin - saying he should resign the party's nomination.
But Akin, who has served six terms, pledged to continue the race against Democratic incumbent Sen. Claire McCaskill.
"The good people of Missouri nominated me, and I'm not a quitter," he said. "And my belief is we're going to take this thing forward and by the grace of God, we're going to win this race."
During the primary campaign, Akin ran TV ads in which Huckabee praised him as "a courageous conservative" and "a Bible-based Christian" who "supports traditional marriage" and "defends the unborn."
Asked in an interview Sunday on KTVI-TV if he would support abortions for women who have been raped, Akin said: "It seems to me, first of all, from what I understand from doctors, that's really rare. If it's a legitimate rape, the female body has ways to try to shut that whole thing down."
Later Sunday, Akin released a statement saying that he "misspoke" during the interview, though the statement did not say specifically which points were in error.
"In reviewing my off-the-cuff remarks, it's clear that I misspoke in this interview, and it does not reflect the deep empathy I hold for the thousands of women who are raped and abused every year," Akin's statement said.
Akin also said he believes "deeply in the protection of all life" and does "not believe that harming another innocent victim is the right course of action."
Brown, considered to be one of the most vulnerable Senate Republicans in the November election, said Akin's comments were "outrageous, inappropriate and wrong."
"There is no place in our public discourse for this type of offensive thinking," said Brown, who is locked in a tight race with Elizabeth Warren.
Brown said Akin should apologize and resign the Senate nomination.
Johnson, a Wisconsin Republican, said in a tweet that Akin "should step aside today for the good of the nation."
Moments after Akin's apology, President Barack Obama said Akin's comments underscore why politicians - most of whom are men- should not make health decisions on behalf of women.
"Rape is rape" Obama said. And said the idea of distinguishing among types of rape "doesn't make sense to the American people and certainly doesn't make sense to me."
The head of the Senate Republicans' campaign arm called Akin's comments "indefensible." Sen. John Cornyn suggested Akin take 24 hours to consider what's best for him.
In a statement issued Monday, Cornyn said Akin should weigh "what is best for him, his family, the Republican Party, and the values that he cares about and has fought for throughout his career in public service."
Akin's remarks also brought a swift rebuke from the campaign of presumptive GOP presidential nominee Mitt Romney and his running mate, Rep. Paul Ryan of Wisconsin.
Romney and Ryan "disagree with Mr. Akin's statement, and a Romney-Ryan administration would not oppose abortion in instances of rape," Romney spokeswoman Amanda Henneberg said.
Romney went further in an interview with National Review Online, calling Akin's comments "insulting, inexcusable and frankly wrong."
"Like millions of other Americans, we found them to be offensive," Romney said.
In an emailed statement Sunday, McCaskill said it was "beyond comprehension that someone can be so ignorant about the emotional and physical trauma brought on by rape."
This month, the 65-year-old congressman won the state's Republican Senate primary by a comfortable margin. During the primary campaign, Akin enhanced his standing with TV ads in which former Arkansas governor and presidential candidate Mike Huckabee praised him as "a courageous conservative" and "a Bible-based Christian" who "supports traditional marriage" and "defends the unborn."
Ushering Akin from the race is complicated by the fact that he has never been a candidate beholden to the party establishment. Since being elected to Congress in 2000, Akin has relied on a grassroots network of supporters. His Senate campaign is being run by his son.
Behind the scenes, Republican officials were looking for intermediaries trusted by Akin to try to coax him from the race.
Missouri election law allows candidates to withdraw 11 weeks before Election Day. That means the deadline to exit the Nov. 6 election would be 5 p.m. Tuesday. Otherwise, a court order would be needed to remove a candidate's name from the ballot.
If Akin were to leave, state law holds that the Republican state committee has two weeks to name a replacement. The candidate would be required to file within 28 days of Akin's exit.
Akin, a former state lawmaker who was first elected to the House in 2000, has a long-established base among evangelical Christians and was endorsed in the primary by more than 100 pastors.
Associated Press writers Henry Jackson in Washington and Chris Blank in Jefferson City, Mo., contributed to this report.