(CNN) In Latin American countries, where abortion is highly restricted if not downright illegal, pregnant women are seeking abortions at significantly higher rates, a new study shows .

This development comes in the aftermath of a November alert about the Zika virus issued by the Pan American Health Organization . The alert revealed the potential for the virus to cause serious complications in unborn children, including microcephaly, severe brain abnormalities, and eye and hearing defects.

Some governments in turn issued health advisory warnings, including the suggestion that women simply avoid becoming pregnant.

This move was unprecedented, said Dr. Catherine Aiken, one of the study's authors. To tell an entire country to simply not get pregnant while not providing access to options -- including, in many cases, contraception -- led her and others to wonder what women were feeling and doing.

"We really were not sure how women were going to respond to this health crisis," said Aiken, a lecturer in the department of obstetrics and gynecology at the University of Cambridge. "The one voice that was missing in the whole conversation was the women themselves."

Seeking online access to abortion medications

In the absence of universal abortion availability, women in Latin America have in recent years turned to Women on Web , a nonprofit that provides online access to abortion medications, specifically mifepristone and misoprostol -- which should not be confused with morning-after pills.

The new analysis of Women on Web's data between January 1, 2010, and March 2, 2016, provided insight into developments in 19 Latin American countries.

What the researchers found was that in places where governments issued health advisories about Zika and pregnancies, requests for abortions through Women on Web jumped by up to 108%. These were not necessarily requests from women who'd even contracted the Zika virus, Aiken said. These were women who feared they might get it.

That largest increase came from Brazil and, not far behind, Ecuador, which had a 107.7% increase. Venezuela's requests grew by more than 93%, Honduras by nearly 76%, Colombia by nearly 39% and Costa Rica and El Salvador by about 36%. Only Jamaica, in this group of countries, saw a decrease in abortion requests, by nearly 33%.

In countries where health advisories were not issued, the numbers generally went up far less, if at all. Bolivia saw the biggest increase, of about 68%. Nicaragua, Panama and Paraguay went up in the range of 21% to 25% and Guatemala by more than 8%. Both Mexico and the Dominican Republic saw decreases in abortion requests by, respectively, about 7% and 20%.

Then there was a group of nearby countries where Zika hadn't shown up when the alert was issued in November. Requests there also went up: in the Bahamas by about 43%, Argentina by about 22%, and Peru and Trinidad and Tobago by about 21%.

All of these stats were tied to Women on Web numbers, however, and therefore probably underestimate the rate of abortions, "since many women may have used an unsafe method, accessed misoprostol from local pharmacies or the black market, or visited local underground providers," the researchers wrote in a letter to the New England Journal of Medicine.

'It isn't enough ... just to warn women'

The World Health Organization predicts that 3 million to 4 million people across North America, Central America, South America and the Caribbean will contract the Zika virus by early next year.

"It isn't enough for health officials just to warn women about the risks associated with Zika," Aiken said. "They must also make efforts to ensure that women are offered safe, legal and accessible reproductive services."

To toss out a terrifying warning without offering ways to help women "harms the health of your population rather than improves it," she said.

Aiken and her colleagues are not alone in believing it's time for serious discussions about women and reproductive rights in Latin America.

Amanda Klasing is a senior researcher with Human Rights Watch who focuses on women in Latin America. Even without seeing this study, she wasn't surprised to hear about the surge in abortion requests.

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Preventing pregnancy can be impossible for some living in this region, she said. Take into account the prevalence of sexual violence and marital rape in the area, or the limited access to contraception, especially for adolescents and marginalized groups.

"Regardless of the fact that you can go to jail for having an abortion in many of these countries, it's not surprising that women and girls would turn to clandestine avenues to procure abortions," Klasing said. "Imagine how scary it must feel to be a girl or woman who becomes pregnant in a Zika-affected country right now."

Those who inevitably suffer most are the poor, who aren't able to work around the system, said Jon O'Brien, president of Catholics for Choice

He doesn't hide his frustration with politicians who answer to church bishops rather than the people they serve. It's on them to "step up to end discrimination against the poor," he said, and make sure all women in Latin America have equal access to legal and safe abortions.

"Politicians in Latin America need to do the right thing," O'Brien said, or they will "forever be remembered as having locked the exit doors as the fire of Zika raged throughout the building."