Secretary of State Brian Kemp declared himself a supporter of a new Mississippi law that bans most abortions after 15 weeks -- the tightest restrictions in the country -- and said he would seek to outdo those limits if elected to Georgia's top job.

In a Tweet and Facebook post late Monday, the Republican candidate said he would "sign the toughest abortion laws in the country as your next governor."

“If abortion rights activists want to sue me...bring it!” he wrote. “I'll fight for life at the Capitol and in the courtroom.”

Kemp’s pledge came hours after Mississippi Gov. Phil Bryant signed the measure, which makes exceptions only for medical emergencies or cases in which there’s a “severe fetal abnormality.” It does not include exceptions for rape and incest, as many other state restrictions do.

Bryant said the legislation helps make Mississippi the "safest place in America for an unborn child." The state's only abortion clinic filed a lawsuit challenging the new rules.

Kemp is one of five leading Republicans in the race to succeed Gov. Nathan Deal, and polls show him in a tight race for the second spot in a likely runoff with Lt. Gov. Casey Cagle.

Another GOP rival adopted a similar position. Former state Sen. Hunter Hill praised Bryant's decision in a tweet and said he would sign "any bill that moves the protection of innocent life closer to conception."

And state Sen. Michael Williams sent a press release Tuesday touting his support for a “heartbeat bill” that bans abortion at six to eight weeks if a heartbeat is detected.

Cagle, meanwhile, said in a statement his “strong pro-life record speaks for itself” and pointed to his support for legislation that made it illegal for Georgia doctors to perform most abortions after 20 weeks of pregnancy.

Businessman Clay Tippins said late Tuesday the Mississippi law “reflects that science increasingly confirms what I have always believed: Life begins at conception."

Two Democrats are also in the race: Former House Minority Leader Stacey Abrams and ex-state Rep. Stacey Evans. Both are outspoken advocates of abortion rights.

More recent AJC coverage of the Georgia governor’s race: