Police removed the 7-year-old girl from her home Monday after spending several hours in the home trying to determine whether she was the biological daughter.
The incident follows a similar case in which a 2-year-old boy was taken from his home overnight before being returned by police, the Irish Examiner reported.
Pavee Point, which advocates for human rights for so-called Irish Travelers, is calling for an independent investigation into the matter, and the girl's parents are supporting the demand, the newspaper said.
Police investigated the girl's family Monday acting on information from a member of the public, the newspaper said.
Waheed Mudah, an attorney for the family, said the parents "believe that there are very serious questions arising about the procedures used in this case."
A spokesman for Ireland's Garda national police said officers followed regulations in removing the girl from her home.
"An Garda Siochana want to assure the community that we take extremely serious all reports received from members of the public concerning child welfare issues. In all cases immediate steps are taken to protect the welfare of the child in accordance with relevant statutory provisions and obligations."
Justice Minister Alan Shatter has asked Garda Commissioner Martin Callinan for a report on the cases of both children, Irish Times reported.
Shatter said police "can be open to criticism for either doing something or doing nothing. In the past, for example, the authorities have been criticized for not intervening to protect children at risk."
The report comes as Greek officials said DNA from a girl found living in a Roma camp in Greece didn't have a match in an international database of missing children.
The non-match intensified efforts to identify the blond-haired girl dubbed "Maria," who was found by Greek police last week during a nationwide crackdown on Gypsies, or Roma, ABC News reported Tuesday.
The initial suggestion about the findings by Interpol is the girl isn't one of the hundreds of children reported missing every year in its database, officials said. The Interpol database doesn't include reports of missing U.S. children.
Maria, believed to be 5 or 6 years old based on a dental exam, is in the care of The Smile of The Child charity at an undisclosed Greek hospital, officials said.
"The kid is happy, plays with her dolls but doesn't seem to like the food that they give her," Costas Giannopoulos, the charity's director told ABC News.
A child psychologist and a Roma translator will interview the girl soon after a court order is issued, Giannopoulos said.
Authorities said they hope genetic testing will reveal the girl's exact age and ethnicity.
Maria was found living with a Roma couple, who first claimed to be her biological parents but later claimed they adopted her "in a non-legal way" from a Bulgarian Roma, attorney Marietta Palavrasa said. They face charges of kidnapping a minor and falsifying documents.
A police source told ABC News the girl was one of four children -- including two other girls and a boy -- found with the couple. The police source said the couple had registered 14 children to receive welfare benefits, but it was unclear whether the other children existed.
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