The Peruvian authorities arrested an American man suspected of running a child-sex ring out of Lima for the past 10 years, the police said Monday. They also said they had rescued 11 victims between 4 and 17 years old, and were investigating the “probable” murders of two children in the case. Gen. Oscar Gonzales, the head of the police unit in charge of human trafficking, said the American, Joshua Brown, 64, of New Hampshire, and five others had been arrested. The police said that Mr. Brown, through a criminal network online, had been offering visitors sex with children for fees starting at $500. “He had a legitimate business in Peru and a parallel dark life,” General Gonzales said. Mr. Brown was in custody and could not be reached for comment. The authorities said he did not have a lawyer.