A group of doctors and women’s rights advocates challenged Arizona’s new abortion limits in a federal lawsuit on Thursday, claiming that they violate the Constitution and pose a threat to women’s health.

The law, set to take effect on Aug. 2, prohibits abortions once 20 weeks have passed since a woman’s last menstrual period, which is about 18 weeks after fertilization. This is the earliest deadline set by any state and is weeks earlier than the threshold set by the Supreme Court.

In Roe v. Wade and related decisions, the court ruled that women have a right to abortion until the fetus is viable outside the womb, often about 24 weeks, and that any ban on later abortions must allow exceptions to protect the life and health of the mother.

The Arizona law allows medical exceptions only in extreme emergencies, when delay would cause the mother’s death or the “irreversible impairment of a major bodily function.”

Thursday’s lawsuit, filed in United States District Court in Phoenix, might bring the first major courtroom test of pre-viability time limits that have recently been adopted in eight other states. They have become a prime tactic of the anti-abortion movement as it seeks to chip away at Roe v. Wade.

Legislators in these states have cited evidence — disputed by major medical societies — that the developing fetus can feel pain.

But the Arizona law sets a limit two weeks earlier than the “fetal pain” laws passed since 2010 in Alabama, Georgia, Idaho, Indiana, Kansas, Louisiana, Nebraska and Oklahoma, said Elizabeth Nash, state issues manager with the Guttmacher Institute, a research group in Washington that supports abortion rights. In the other states, the deadline is 20 weeks after fertilization, not the last menstrual period.

“This is the most extreme example yet of these early-limit laws,” said Nancy Northup, president of the Center for Reproductive Rights, which brought the lawsuit along with the American Civil Liberties Union and three doctors in Arizona who said the law would interfere with patient care.

“This law also has a radically limited health exception that is completely unacceptable under the constitutional standard,” Ms. Northup said. “A woman has to be in a dire emergency to have an abortion.”

Cathi Herrod, president of the Center for Arizona Policy, a conservative Christian group that helped write the law, said it was needed to protect the health and safety of women and protect “pre-born children” from pain and death.

Dr. Paul A. Isaacson, a gynecologist in Phoenix who offers family planning and abortions and is a plaintiff in the lawsuit, said the new law would “profoundly affect some of my patients.”

Most women seeking later abortions, he said in testimony against the bill last spring, “do so because they have received a diagnosis of a severe fetal anomaly during the course of a wanted pregnancy.” Often, he said, fetal problems cannot be diagnosed before 20 weeks of pregnancy.

The new law, he said, would force some women to carry pregnancies to term even when it is clear that the newborn will quickly die, “often at substantial health risks to themselves.”

Women, their families and their doctors should make these wrenching decisions, Dr. Isaacson said, not the Legislature.

Ms. Northup, of the Center for Reproductive Rights, said that the pre-viability time limits in Arizona and other states were clearly unconstitutional and that she expected the new case to set an important precedent. The plaintiffs are seeking a preliminary injunction to delay enforcement of the law and will appeal any adverse decisions, she said.

Ms. Herrod, the law’s proponent in Phoenix, said that courts had given states the right to protect women and fetuses.

“We are very hopeful the courts will uphold this law,” she said, vowing equally to fight this case to the end.