A U.S. federal consumer protection agency filed a complaint against e-commerce giant Amazon on Thursday, alleging the company is illegally billing parents for their children's unauthorized in-app purchases.

The Federal Trade Commission (FTC) accused Amazon of violating the FTC Act by billing parents for charges incurred by their children when making purchases within apps on mobile devices without parental consent.

The agency is seeking a court order requiring Amazon to refund millions of U.S. dollars to consumers affected by the charges.

When Amazon first introduced in-app purchases, children playing games offered in the Amazon app store could spend money on virtual items within the apps without their parents' authorization.

Amazon changed the in-app charge system in March 2012 to require consumers to enter a password, however this only applied to individual purchases over 20 U.S. dollars. The FTC's complaint notes that Amazon continued to allow children to make an unlimited number of purchases under that amount without a parent's approval.

In early 2013, Amazon updated the system again, adding the requirement of a password for individual in-app charges of less than 20 dollars. But according to the complaint, consumers were not informed that entering the password would leave open a window of up to one hour, in which children could make unlimited purchases without further authorization.

While Amazon did make changes last month to require account holders' consent for each in-app purchase, thousands of parents complained to Amazon about charges their children incurred during the past two and a half years, according to the complaint.

"Amazon's in-app system allowed children to incur unlimited charges on their parents' accounts without permission," said FTC Chairwoman Edith Ramirez in a press release.

Knowing a lawsuit would be launched, Amazon sent a letter to the FTC early this month, saying it would defend its approach in court.

Earlier this year, the FTC filed a similar complaint over children's in-app purchases against Apple. The tech giant settled with FTC for 32.5 million dollars, to be used to refund consumers. Endi