The Federal Trade Commission sued Amazon on Thursday for allowing children to make purchases within mobile applications even though the company knew that kids were doing so without parental permission.

The suit, filed in federal court in Seattle, alleges that the online retail giant knowingly allowed kids to run up “millions of dollars” of charges buying virtual items within the gaming apps such as “coins,” “stars” and “acorns,” all without parental involvement.

“Companies need to get consumers’ consent before placing charges on their bills,” Jessica Rich, director of the agency’s consumer protection bureau, said in a conference call with journalists.

Amazon declined to comment on the suit, except to reiterate comments that its lawyer, Andrew C. DeVore, made in a letter to FTC Chairwoman Edith Ramirez last week. Then, DeVore disputed the claims and described litigation as “an unfortunate misallocation of the Commission’s resources.”

The dispute stems from gaming apps that Amazon sells from its Appstore to consumers, who then play them on mobile phones or tablets. The apps, which target children, such as Pet Shop Story and Ice Age Village, aren’t made by Amazon. But Amazon receives 30 percent of all revenue from in-app purchases.

When Amazon introduced in-app purchases in November 2011, it didn’t require any passwords to make in-app purchases. Soon afterward, an Amazon Appstore manager described the level of complaints about unauthorized purchases as “near house on fire,” according to the suit.

Amazon updated its policy in March 2012 to require authorization for in-app purchases above $20.

At the time, an Appstore manager wrote in an internal document obtained by the FTC that “it’s much easier to get upset about Amazon letting your child purchase a $99 product without any password protection than a $20 product.”

“Over time, Amazon changed its in-app charge process, but it did not fix the problem, and it was not transparent with consumers,” Rich said.