Researchers emphasize that it is too early to give pregnant women any specific advice based on the results.
Moreover, the study does not implicate folic acid use in early pregnancy.
This is an important finding, note the researchers, because adequate folic acid around the time of conception helps lower the risk of certain birth defects of the brain and spine. Known as neural tube defects, these anomalies include spina bifida, a paralyzing defect of the spine, and anencephaly, a fatal defect where most or all of the brain fails to develop.
Experts advise women to take 400 micrograms of folic acid per day shortly before conceiving and in the first trimester of pregnancy, a critical window of time when neural tube defects take shape.
The current findings "don't contradict" that advice, lead researcher Dr. Michael Davies, of the University of Adelaide in Australia, told Reuters Health in an email.
However, he added, since folic acid is necessary only in the first trimester to prevent neural tube defects, further studies should look at whether more-specific guidelines on folic acid use during the remainder of pregnancy can and should be developed.
For their study, Davies and his colleagues looked at asthma rates among more than 400 children whose mothers had been followed since pregnancy. A little less than 12% of the children had developed asthma by age 3, and the same percentage had the lung disease at age 5.
Overall, the study found, children whose mothers took folic acid in late pregnancy - from the 30th week on - were one-quarter more likely to have asthma at age 3 compared with children whose mothers did not take folic acid at that point in pregnancy.
They were also more likely to have persistent asthma symptoms from the age of 3 through age 5.
Most mothers who took folic acid in late pregnancy did not take it as a stand-alone supplement, but as part of a multivitamin; they typically got 300 micrograms of folic acid per day from supplements.
There was no link between mothers' folate intake from food and their children's asthma risk; folate is the natural form of folic acid, found in foods such as beans and lentils, orange juice, peanuts and green vegetables like spinach and broccoli.
That latter finding, Davies noted, should encourage women to eat a healthy diet, including folate-rich foods, throughout pregnancy.
It is not entirely clear why folic acid supplements in late pregnancy would promote asthma in some children. However, Davies pointed to recent animal research suggesting that folate can alter the activity of immune-system-regulating genes in the lung tissue - potentially making it more susceptible to allergic reactions.
Since the fetal immune system develops later in pregnancy, folic acid use at this point could theoretically affect a child's future risk of asthma.
Davies stressed, however, that a single study is rarely enough to change health policies and practices.
"We would like to see systematic replication of our findings and clinical trials in various populations," he said, "so that we can provide appropriate, refined and targeted advice."