The study, sure to renew controversy over the safety of mobile telephones, does not demonstrate that cellphone use causes the behavioral problems and does not suggest a possible way that they could.
But the researchers say their findings are worth checking out.
"It is hard to understand how such low exposures could be influential," Dr. Leeka Kheifets, an epidemiologist at the University of California Los Angeles who led the study, said in a telephone interview.
"It is just something that needs to be pursued."
Kheifets and her team looked at data from 28,000 7-year-olds and their mothers who took part in a large Danish study that has been tracking 100,000 women who were pregnant between 1996 and 2002.
The mothers of about 3 percent of the children said they had borderline behavioral problems, and 3 percent showed abnormal behavior, such as obedience or emotional issues.
The children whose mothers used cellphones while pregnant and who also used the phones themselves were 50 percent more likely to have behavioral problems, the researchers reported in the Journal of Epidemiology and Community Health.
Children whose mothers used the phones but who did not themselves use mobile phones were 40 percent more likely to have behavioral problems, they found. They found the children were no more likely to have epilepsy or delays in development.
About 5 billion mobile phones are in use worldwide. The World Health Organization, the American Cancer Society and the National Institutes of Health have found no evidence that cellphone use can damage health.
Last May, experts who studied 13,000 cellphone users over 10 years hoping to find out whether they cause brain tumors found no clear answer.
International researchers launched the biggest study to date into mobile phones and health in April.
Kheifets tried to account for other possible causes, such as whether women who used cellphones were different from women who did not, especially during the time of their pregnancies when cellphone use was less common than it is now.
"We looked at social status, we looked at the sex of the child, we looked at the mother's history of behavioral problems, we looked at the mother's age and stress during pregnancy and whether the child was breastfed or not," she said.
"One thought was that it was it not cellphone use but mothers' inattention that led to behavior problems. While it was important, it didn't explain the association that we found."
Nonetheless, some experts questioned the findings.
"I am skeptical of these results, even though they will get a lot of publicity," said David Spiegelhalter, a professor of Biostatistics at Britain's University of Cambridge.
"The authors suggest that precautionary measures may be warranted because they have 'virtually no cost', but they ignore the cost of giving intrusive health advice based on inadequate science."
Experts at the U.S. National Institutes of Health had no immediate comment.
John Walls of the mobile telephone industry group CTIA noted that other studies ave failed to show a health risk from cellphones. "We just don't comment on any specific studies because we don't have any expertise, frankly," Walls said in a telephone interview.