Costa, who was speaking to a parliamentary committee, gave no indication how the investigation would end but said it was "premature" to say it had failed.
Portuguese police have laid no formal charges in the case of the girl, who disappeared in the Algarve on May 3. They have named the three-year-old's parents, Kate and Gerry McCann, as suspects in the disappearance.
"We are in a phase in which we are approaching the conclusion of this case," Costa said.
Portuguese police have faced criticism in the media for making no progress in finding the girl.
"I think the suggestion of failure is premature," Costa said.
At the beginning of this month, the head of Portuguese police, Alipio Ribeiro, said authorities had been hasty in naming the McCanns as suspects.
Costa said there was no impact on the investigation from Ribeiro's comment, which prompted the McCanns to urge Portuguese police to drop them as suspects and focus on finding their missing daughter.
