WASHINGTON—The Federal Trade Commission sued T-Mobile US Inc. on Tuesday, accusing the wireless carrier of adding hundreds of millions of dollars in bogus charges to subscribers' bills as recently as December.

In a civil complaint filed in federal court in Seattle, the FTC alleged that T-Mobile charged consumers monthly fees for third-party services that in many cases the subscribers hadn't ordered. These included ringtones, wallpaper, and text messages providing celebrity gossip and horoscopes, the agency said.

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