The couple have been placed in detention pending a trial.
Maria was found during a raid on a Roma camp in central Greece last week.
DNA tests showed that she was not related to the couple, who insist they were given her legitimately.
Maria is being cared for by a charity in Athens, which has received more than 8,000 calls after an appeal.
The Roma couple appeared before judges on Monday to answer charges of abducting a minor and holding false papers.
The 39-year-old man and 40-year-old woman were identified by Greek police as Christos Salis and Eleftheria Dimopoulou.
The Roma community where the girl was found has rallied around the couple, saying they looked after her well.
The head of the Roma association in Farsala in central Greece says the pair treated her better than their biological children and that she loved them.
Ahead of Monday’s hearing, a lawyer representing the Roma couple, Kostas Katsavos, said that they were carrying out a search for the girl’s mother.
He said the couple claim the woman had given Maria to them because she could not look after her daughter.
“Our clients’ claim is that <<we never abducted this child, we just adopted her>> in a way that was not legal, that we can confess,” said Kostas Katsavos.
But the couple are suspected by social workers of kidnapping the girl and sending her out to beg.
Police initially raided the Roma camp to search for drugs and weapons.
They noticed the lack of resemblance between the blonde-haired, blue-eyed, pale-skinned little girl and her parents, and found further discrepancies when they investigated the family’s documents.
The couple had registered different numbers of children with different regional family registries.
The Greek authorities say the couple were in possession of false papers which suggested the woman had given birth to six children within a 10-month period.
When questioned about how they came to have Maria, the couple made “constantly changing claims”, Thessalia Province Police Director Vassilis Halatsis said.
Through Interpol, Greece has requested assistance from other European countries.
Police decided to appeal internationally as the girl looked as if she might be from northern or eastern Europe.
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