A private investigator hired by Kate and Gerry McCann believes their missing daughter Madeleine was kidnapped by a pedophile ring in the Iberian Peninsula or northern Africa, and that she will be returned by Christmas, the Daily Mail reported.

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"I cannot say who she is with because we are putting together conclusive proof we can present to the authorities so they can proceed with their arrests," Francisco Marco is quoted telling the Spanish newspaper Metro.

Marco promised last month that he would find Madeleine, 4, who disappeared May 3 from a vacation apartment in Portugal.

Marco heads up the Barcelona-based Metodo 3, which has been working for the McCanns since September, the Daily Mail reported. Metodo 3 has been criticized by Portuguese police as "small fry" and "irrelevant," the newspaper reported.

"I have always said publicly Madeleine is alive," Marco reportedly told Metro. "I have to believe it 100 percent because I know how to look for living people, not dead ones. But I have no proof Madeleine is alive.

"We have proof of her movements after her kidnap and we know she was alive the day after her disappearance. We are not certain she left Portugal.

"I talk of certainties because we know which group may have her or could have kidnapped her to then sell her on to others," Marco said.