EL CAJON, Calif. >> “Free Pregnancy Testing,” reads the large sign in front of the East County Pregnancy Care Clinic, on a busy intersection of this impoverished city east of San Diego.

Inside the clinic, a woman will not only get a free pregnancy test, but she will also see a counselor to discuss her options. She will see models of fetuses at early stages of development, which show that “at week 12, you see a recognizable human,” said Josh McClure, executive director of the clinic. If she is pregnant, she can get a free ultrasound and attend childbirth classes. If she gives birth, she may receive help with diapers and a car seat.

What she will not get from this center is advice on where to obtain an abortion.

The clinic is one of more than 3,000 crisis pregnancy centers around the country that are operated by religious opponents of abortion, with the heartfelt aim of persuading women to choose parenting or adoption. Now it and others in California are in a First Amendment battle with the state over a new law that requires them to post a notice that free or low-cost abortion, contraception and prenatal care are available to low-income women through public programs, and to provide the phone number to call.

The clinics argue that the law, which took effect in January, flagrantly violates their rights of free speech, and it appears that many of the dozens of licensed pregnancy centers in California are not yet complying.

“I don’t want to put up a sign telling you where you can go for an abortion,” said McClure of the clinic here, which is a plaintiff in one of several legal challenges. “The sign is not up here now because it’s unconstitutional.”

Many states are passing restrictions that could force abortion clinics to close, a tactic under scrutiny in a major Supreme Court case to be argued next month. Here in California, it is the abortion opponents who are seeking to block a law — one adopted by a liberal state government to offset what officials call the misleading advice dispensed by pregnancy centers.

Abortion rights advocates have long accused the centers of luring women in without revealing their bias, then providing false accounts of medical and emotional risks of abortion, among other tactics, to steer them away from the procedure. But the Constitution’s high bar for interfering with free speech has largely protected the centers from regulation. Previous efforts in New York City and a few other places to require them to state, upfront, that they do not provide abortion referrals and make other disclosures have been largely struck down by federal courts.

So far, California’s law has fared better, with three federal district courts and one state court refusing to block it as the cases proceed toward trial. Officials say their law is written to comply with the First Amendment because it does not force the centers to say anything about their beliefs. Rather, it requires licensed centers to prominently post, or hand out, factual notices about public programs.

According to NARAL Pro-Choice California, whose investigation of pregnancy centers was cited by legislators, around 170 to 200 such centers are operating in California. At least 70 are licensed, meaning they are under the supervision of a physician and employ nurses and volunteer counselors.

The rest are unlicensed. In a twist of First Amendment law, it is harder to justify regulating their speech than it is to oversee the statements of state-sanctioned professionals. So the law simply requires these centers to post that they are not licensed.

On Jan. 28, in the third such effort in a federal court, a lawyer from Alliance Defending Freedom, a conservative legal group that is representing the El Cajon clinic and others, argued in San Diego for a preliminary injunction.

In the 90-minute hearing, Matt Bowman, a lawyer for the conservative group, argued that the law imposes an onerous and unconstitutional burden. “You’ve got to give women information about abortion even though the reason you exist is to give them alternatives to abortion,” he said, arguing against the mandate.

Anthony Hakl, a deputy attorney general, replied that “the interest of the state is compelling — that is to ensure women’s access to a complete range of reproductive health services.”

On Tuesday, Judge John A. Houston, who in the hearing had suggested that the notices may be essential to “an informed decision,” became the third federal judge to refuse to grant the preliminary injunction requested by the pregnancy centers. In the previous two cases, the federal appeals court had also refused to block the law.

McClure denied that the center in El Cajon tries to mislead anyone, saying it provides honest information that allows women to make their own decisions.

The clinic was established by evangelical churches in 1993; its annual budget, close to $300,000 in 2014, is met with donations from churches, individuals and businesses.

In 2015, McClure said, the clinic served 674 clients — 32 percent Caucasian, 29 percent Hispanic, 12 percent African-American and 15 percent Arabic, drawn from the population of Iraqi and Chaldean refugees in El Cajon. Close to half were unmarried.

More than one in three clients were initially considering an abortion, he said, but all but a small percentage ended up deciding to give birth. By around 12 weeks of pregnancy, he said, women are referred to doctors for prenatal care.

The clinic has one nurse manager and about 10 nurse volunteers. Volunteer counselors first take women into a small room to discuss why they have come, and describe the options of parenting, adoption and abortion.

Beyond assistance for needy new mothers, the center also gives advice on how to avoid another pregnancy: abstinence for the unmarried, “natural” methods for the married.

Many centers across the country provide what mainstream medical experts say are misleading accounts of rare abortion complications, and of disproved longer-term effects. The centers often suggest, for example, based on what critics describe as a selective or outdated review of research, that abortion raises the risks of premature births, depression and breast cancer.

Some written materials of the El Cajon clinic describe the evidence on breast cancer as “disputed,” while at least one brochure in the facility flatly says that abortion causes “an increased risk of breast, cervical and ovarian cancer.”

“We believe there is a link,” McClure said of the breast cancer claim.

But the National Cancer Institute states that “women who have had an induced abortion have the same risk of breast cancer as other women,” and that abortion has not been linked to other cancers, either.

The court battles appear likely to continue over the next year. The legal groups representing the centers, which also include the Pacific Justice Institute and the American Center for Law and Justice, vow to pursue the issue to the Supreme Court.

Things may come to a head sooner. The office of Kamala D. Harris, the California attorney general, who strongly supports the law, would not comment on enforcement. But NARAL Pro-Choice California said that it plans to monitor compliance and urge city and county lawyers to act.

© 2016 The New York Times Company