“It’s clear that many companies are violating that law,” Mr. Markey said in a phone interview, “and that we need to put a spotlight on it and ensure that that type of activity is stopped cold.”

The letter cited a New York Times article published last month that described how multiple children’s apps sent personal information, including precise location and tracking ID numbers, to outside companies. The apps, with names like Fun Kid Racing and Masha and the Bear: Free Animal Games for Kids, offered animated games and videos. Many of them are so simple a toddler could play them.

The Times also found programs in Google’s Play store and Apple’s App Store that were labeled appropriate for children but, once downloaded, sent personal data without verifiable parental consent. Apps on the Apple platform sent less data over all.

Those findings were consistent with academic research published this year. The researchers analyzed nearly 6,000 free children’s Android apps and found that more than half shared data in ways that could violate the law.

Last month, the New Mexico attorney general sued the maker of Fun Kid Racing, along with online ad businesses run by Google, Twitter and three other companies. The suit accused the companies of violating the children’s privacy law. It also argued that Google misled parents by allowing the apps to remain in the children’s section of its store and failed to act swiftly when researchers contacted the company with concerns that thousands of apps might be improperly tracking children.