Police have said they suspect records that the couple provided for Maria and for other children in their care may be false. In addition to the abduction charge, the couple is accused of falsifying official documents.
Four authorities, including the head of the registry office that issued Maria's birth certificate, have been suspended while a police investigation is under way, the media office of the Athens municipality said Tuesday.
The girl received the document this year, it said. It is unusual for a birth certificate to be issued years later.
Authorities asked questions about Maria because she has fair skin and blond hair, while her parents have darker complexions typical of Roma, a people descended from Indian nomads, who face widespread discrimination in Europe.
Their lawyers say they took Maria into their home after her biological mother, who they say was from Bulgaria, was unable to look after her.
CNN's Karl Penhaul spoke with residents of the Roma community who backed that assertion.
"Maria used to play here with the other children and go to the store with her mum. Maria was not hidden away," Maria Kaleas said. "The mother gave her away and Eleftheria was enchanted by Maria's beauty. She shared the food for her own children with Maria."
Could 'Maria' be an American girl?
Thousands of calls poured into Greece after authorities released photos of the girl last week.
Deborah Bradley and Jeremy Irwin, whose daughter Lisa Irwin was 11 months old when she vanished two years ago from their home in Kansas City, Missouri, asked the FBI to contact Greek authorities about the case.
"There is no such thing as a tip too small," said Bradley, whose hopes were raised despite the apparent disparity in age between their missing daughter and Maria.
A federal law enforcement official said the FBI is working with Greek authorities to determine whether the girl could be Lisa Irwin.
A top official with the National Center for Missing & Exploited Children in Virginia said the center works with law enforcement groups to collect data, biometrics information and DNA that can be used to compare with samples from Maria.
"Frankly, right now ... it does not appear that this may be any of our children. But again we want to confirm one way or the other," said Robert Lowery, the senior executive director of the organization's missing children division.
He added that a definitive comparison could be done "rather quickly."
Prejudice against the Roma
Prejudice and discrimination against the Roma are widespread in Greece and elsewhere in Europe, Amnesty International says.
Maria's case plays into old prejudices about them stealing children for forced labor.
Pardalis mentioned such a possibility, saying, "We don't have any other information if this girl was forced to work or to beg on streets."
The government news agency also raised "the possibility of the existence of a ring bringing pregnant women to Greece from Bulgaria and then taking their children for sale." The agency cited past reports that empty coffins had been found for infants who supposedly were stillborn to foreign mothers in Athens.