WASHINGTON — A federal judge will not dismiss the Federal Trade Commission’s lawsuit against Amazon.com over the company’s practice of billing parents for in-app purchases their children made without parental approval.

The lawsuit alleges that Amazon failed to stop children from spending millions of dollars of their parents’ money for virtual items in online games and other apps on devices such as Amazon’s Kindle Fire tablet. Some of the purchases cost as much as $100 each.

Amazon argues that it adequately warns customers when an app allows for in-app purchases. It also says the FTC could not prove that the bills the children racked up were “unauthorized” by parents.

Judge John Coughenour disagreed with Amazon’s reasoning Monday, saying the retail giant may still have violated federal laws against unfair billing, whether the charges were authorized or not. In any event, Coughenour said, it is Amazon’s responsibility to prove that the charges were authorized, and it has not done that.

“Though notice of in-app purchases and the possibility of parental controls may have enabled some customers to avoid in-app purchases,” Coughenour wrote, “the facts presently before the court do not suggest so much care and clarity as to warrant dismissal. The FTC has sufficiently alleged that the injury to Amazon customers was not reasonably avoidable.”

The ruling means the FTC’s lawsuit can move forward.

An Amazon representative did not respond to a request for comment.