NEW YORK — The operator of fan websites for pop stars Justin Bieber, Selena Gomez, Rihanna, and Demi Lovato agreed to pay a $1 million civil penalty to settle federal charges that the sites had illegally collected personal information about thousands of young children, the Federal Trade Commission said Wednesday.

In a complaint, the FTC alleged that Artist Arena, the operator of the sites, had violated a children’s online privacy rule by collecting personal details — like the names, e-mail addresses, street addresses, and cellphone numbers — of about 101,000 children aged 12 or younger without their parents’ permission.