Pregnant women have long been assured that acetaminophen can treat their aches, pains and fevers without bringing harm to the babies they carry. Now researchers say they have found a strong link between prenatal use of the medication and cases of attention-deficit hyperactivity disorder in children.

The results, published in the journal JAMA Pediatrics, add to growing evidence that the active ingredient in Tylenol may influence brain development in utero.

But they do not provide clear answers for mothers-to-be or their doctors about whether acetaminophen is safe during pregnancy.

In analyzing data on more than 64,000 Danish women and their children, researchers found that children whose mothers took the painkiller at any point during pregnancy were 29 percent more likely to be diagnosed with ADHD than were youngsters whose mothers took none.

The risk increased the most — by 63 percent — when acetaminophen was taken during the second and third trimesters, and by 28 percent when used in the third trimester alone. But when taken only in the first trimester, the added risk was only 9 percent.

The findings do not establish that prenatal exposure to acetaminophen — which is also an ingredient in Excedrin — caused the observed increase in hyperactivity disorders.

But they underscore that medications are only “safe” for pregnant women until studies become sensitive enough to detect subtle problems, said Dr. Daniel Kahn, an obstetrician who was not involved in the research.

An editorial published alongside the report cautioned that physicians and pregnant women would be wrong to change their practices on the basis of one study alone.