Planned Parenthood, a non-profit organization, tweeted, 'This is a devastating blow to the 4 million patients who obtain birth control, cancer screenings through Title X'
The lawyers added that "many of the laws are so vaguely written" anyone involved in the abortion process could be prosecuted.
A 2005 survey, which backs abortion rights, found about 1 per cent of women said they had abortions because of rape or incest.
More than a dozen states have adopted laws banning or drastically curtailing access to abortion which was legalized in the landmark 1973 US Supreme Court ruling Roe v Wade.
Women's reproductive rights defenders will gather to denounce the "Alabama Human Life Protection Act," or HB314, which virtually outlaws terminations.
Mace is against abortion in most cases and supported the fetal heartbeat bill as long as it contained the exception for rape and incest.
Alabama passed a law banning women from having an abortion even in cases of incest or rape and the Missouri legislature made illegal abortions from eight weeks of pregnancy.
Planned Parenthood Action Fund President Leana Wen said in a statement that enacting the measure would be disastrous.
Georgia's "heartbeat bill" would ban abortion once a fetal heartbeat is detected, which can be as early as six weeks, before many women know they are pregnant.
If a new Mississippi law survives a court challenge, it will be nearly impossible for most pregnant women to get an abortion there.