The Federal Trade Commission is suing Amazon.com, alleging that the online retailer unlawfully billed parents millions of dollars for mobile in-app purchases made by their children.

The federal complaint, which was filed in Washington’s District Court on Thursday, asks for a court order requiring Amazon to refund customers for unauthorized charges and to ban the company from billing parents for in-app charges made by children without their consent.

According to the complaint, many of the kid-friendly games and apps on Amazon mobile devices, such as the Kindle Fire, encourage children to pay for virtual in-game items with real world money, usually connected to their parents’ bank accounts.

Amazon, which, according to the complaint, collects 30 percent of all in-app charges, allegedly did not require password certification on in-app purchases when the company began the service in November 2011.

Thousands of parents have complained to Amazon about in-app purchases made by children, according to the complaint.

In a letter sent to the FTC on July 1, an attorney for Amazon said the FTC was seeking an arrangement similar to the one that the regulatory body made with Apple in January.

Under that deal, Apple refunded around $32.5 million to consumers for charges in mobile applications and changed billing practices to ensure that customers consent to purchases.

Amazon said it has improved the in-app buying process and already offers refunds when children make inadvertent in-app purchases.

“Pursuing litigation against a company whose practices were lawful from the outset and that already meet or exceed the requirements of the Apple consent order makes no sense,” Amazon said.