AUSTIN, Texas — Gov. Greg Abbott, responding to a question about how Texas' new abortion law would impact victims of rape and incest, said the state would employ aggressive tactics to "eliminate all rapists from the streets of Texas."

The law, which took effect last week, bans abortion after about six weeks of pregnancy and allows private citizens to sue people who aid or abet an abortion in violation of the law. It does not include exceptions for victims of rape or incest, a caveat often included in abortion restrictions.

"Rape is a crime, and Texas will work tirelessly to make sure that we eliminate all rapists from the streets of Texas by aggressively going out and arresting them and prosecuting them and getting them off the streets," Abbott said on Tuesday, responding to a question from a reporter after he signed the divisive GOP elections bill into law.

Abbott faced immediate blowback for the comment from critics of the ban, who said his promise was not rooted in reality.

"NEWSFLASH: Rape has been a crime in TX and it still hasn't been eliminated," state Rep. Jasmine Crockett, D-Dallas, said in a tweet. "There is no magic wand to eliminate any crime!"

U.S. Rep. Lizzie Fletcher, D-Houston, told MSNBC on Tuesday that she would "love to see Texas address violence against women," but said that is not what this legislation does.

"It's kind of this magical thinking that's typical of his approach to governing, that he'll give an answer that is really untethered to the reality of what he's doing," she said. "We know that Texas, unfortunately, has not been making this its top priority."

Abbott's office did not return a request for information about how he planned to carry out his promise.

"Maybe Governor Abbott should have eliminated rape and incest BEFORE passing an abortion law that didn't have an exception for rape and incest?" state Rep. Gene Wu, D-Houston, in a tweet on Wednesday.

He followed it with another: "Just a reminder — (Texas Republicans): PASSED a law putting a $10,000 bounty on people who help victims of rape with an abortion. DID NOT put a $10,000 bounty on RAPISTS."

Texas' abortion law does not allow public officials to enforce the ban and instead allows any private citizen to sue abortion providers, staff at clinics or someone who drives a patient to receive their procedure — anyone who could be seen as aiding and abetting an abortion in violation of the law.

If these private individuals are successful in a lawsuit, they can collect at least $10,000 in damages from the defendant, plus a reimbursement of legal fees.

Some Republicans came to Abbott's defense on Wednesday, including state Rep. Matt Schaefer, R-Tyler. He responded to Crockett's tweet criticizing Abbott and said: "Is it humane to kill an innocent person because of the violent crime of another person?"

During the Tuesday event, Abbott pushed back at a description of the abortion ban offered by a reporter, who asked why the state would want to "force a rape or incest victim to carry a pregnancy to term."

"It doesn't require that at all, because obviously it provides at least six weeks for a person to be able to get an abortion," Abbott said.

That remark also drew criticism from both opponents of the ban, who say that it prohibits the procedure before most women are aware they are pregnant, and from one of Abbott's Republican challengers: former state Sen. Don Huffines.

Huffines said in a statement that it was "disgusting" to see Abbott "advocating for women to get abortions."

"The pro-life response should always be to acknowledge the human value of all unborn children, and today (Abbott) fell short of that very clear standard," he said.