"But I would certainly rather it come to my desk with an exception for rape and incest," Barbour told the AP. "I think that's consistent with the opinion of the vast majority of Mississippians and Americans."
No lawmakers stood to argue in favor of abortion rights, although several said abortions should be allowed if a woman was impregnated against her will.
A Missouri bill, sponsored by Republican Sen. Jason Crowell, would make it a felony charge for anyone who performs an abortion, carrying a sentence of five years to 15 years in prison.
"Across the country, state politicians are creating a gauntlet of anti-choice laws and regulations to make it more difficult for women to get the best and safest reproductive health-care services," Eve Gartner, senior staff attorney for Planned Parenthood, said in a statement following the South Dakota ban. "South Dakota's ban is the most sweeping abortion ban passed by any state in more than a decade. Planned Parenthood will go to court to ensure women, with their doctors and families, continue to be able to make personal health-care decisions -- not politicians."
Nationwide, abortion opponents are split over whether it's time to pull out all the stops on banning abortion or time to continue seeking to restrict the procedure with less ambitious bills, such as measures to require parental consent or regulate clinics.
"The pro-life community is divided on what the best strategy is," said Sam Lee, of the anti-abortion group Campaign Life Missouri.
ABCNEWS.com's Rose Palazzolo contributed to this report.