NEW YORK — A puzzling study of U.S. pregnancies found that women who had miscarriages between 2010 and 2012 were more likely to have had back-to-back annual flu shots that included protection against swine flu.

Vaccine experts think the results may reflect the older age and other miscarriage risks for the women, and not the flu shots. Health officials say there is no reason to change the government recommendation that all pregnant women be vaccinated against the flu. They say the flu itself is a much greater danger to women and their fetuses.

The Centers for Disease Control and Prevention has reached out to a doctor’s group, the American Congress of Obstetricians and Gynecologists, to warn them the study is coming out and help them prepare for a potential wave of worry from expectant moms, CDC officials said.

“I want the CDC and researchers to continue to investigate this,” said Dr. Laura Riley, a Boston-based obstetrician who leads a committee on maternal immunization. “But as an advocate for pregnant women, what I hope doesn’t happen is that people panic and stop getting vaccinated.”

Past studies have found flu vaccines are safe during pregnancy, though there’s been little research on impact of flu vaccinations given in the first three months of pregnancy.

This study focused only on miscarriages, which occur in the first 19 weeks of pregnancy and are common. As many as half of pregnancies end in miscarriage, according to a March of Dimes estimate that tries to include instances in which the miscarriage occurs before a women even realizes she was pregnant.

Flu and its complications kill thousands of Americans every year. The elderly, young children and pregnant women are especially at risk. When a new “swine flu” strain emerged in 2009, it killed 56 U.S. pregnant women that year, according to the CDC.