PIERRE, S.D. — Women seeking an abortion in South Dakota will face the longest waiting period in the nation — three days — and have to undergo counseling at pregnancy help centers that discourage abortions under a measure signed into law Tuesday by Gov. Dennis Daugaard.

Within minutes of Daugaard’s announcement that he had signed the measure, abortion rights groups said they plan to file a suit challenging the measure, which one said could create particular hardships for women who live in rural areas hundreds of miles from the state’s only abortion clinic in Sioux Falls.

Daugaard, a Republican, who gave no interviews after signing the bill, said in a written statement that he had conferred with state attorneys who will defend the law in court and a sponsor who has pledged to raise private money to finance the state’s court fight. Officials have estimated the cost of defending the law at $1.7 million to $4.5 million.

“I think everyone agrees with the goal of reducing abortion by encouraging consideration of other alternatives,” he said in the statement. “I hope that women who are considering an abortion will use this three-day period to make good choices.”

About half the states, including South Dakota, now have 24-hour waiting periods, but the state’s new law is the first of its kind in having a three-day waiting period and requiring women to seek counseling at pregnancy help centers, said Elizabeth Nash of the Guttmacher Institute, a research organization that supports abortion rights.

The law will certainly make it harder for some women to get abortions, said Kathi Di Nicola, a spokeswoman for Planned Parenthood Minnesota, North Dakota and South Dakota, which runs the clinic in Sioux Falls. Women could have to drive there several times to schedule an abortion, visit a crisis pregnancy center and then get an abortion, Di Nicola said.

“It would most certainly be a barrier to women who have to travel. South Dakota is a rural state,” she said. “Many women who are seeking abortion care already have to take time off work, arrange for child care.”

Planned Parenthood and the American Civil Liberties Union of South Dakota said they will ask a judge to strike down the measure as unconstitutional.

The measure’s backers say the Planned Parenthood clinic gives women little information or counseling before they have abortions done by doctors flown in from out of state, and the bill will help ensure that women are not being coerced into abortions by boyfriends or relatives.

“Women need to just be reminded of the fact there is a natural, legal relationship between them and their child,” said Rep. Roger Hunt, R-Brandon, main sponsor of the law.

The law, which takes effect July 1, says an abortion can be scheduled only by a doctor who has personally met with a woman and determined she is voluntarily seeking an abortion. The procedure can’t be done until at least 72 hours after that first consultation.

Before getting an abortion, a woman also will have to consult with a pregnancy help center to learn about its services. The state will publish a list of pregnancy help centers, all of which seek to persuade women to give birth.

Leslie Unruh, founder of the Alpha Center, a Sioux Falls pregnancy help center, said many women have said they would never have had abortions if they had first received counseling at such a center.

Jan Nicolay, co-chair of the South Dakota Campaign for Healthy Families, which has opposed restrictions on abortion, said the measure would invade women’s privacy by forcing them to go to crisis pregnancy centers, which are set up to dissuade women from getting abortions. The law could violate federal requirements that protect the privacy of medical records, and it assumes that women cannot make decisions about abortions after talking with their families and pastors, she said.