In a case which has gripped the country, two couples are fighting for the custody of the babies born on Sunday whose fertilised embryoes were mixed up in a Rome hospital.
The families have very similar names, sharing five of seven letters, according to La Repubblica newspaper.
The mother who carried the baby has refused to give up the children, but the couple still intend to sue and file charges against the hospital, their lawyer Michele Ambrosini said.
Judge Silvia Albano told an hour-long hearing on Friday that he needed more time to consider whether the biological parents had the right to demand custody of the children.
The error was not noticed until the mother who gave birth to the twins had a genetic test at three months to check for illness which revealed neither she nor her partner were the biological parents.
When the babies were born at the weekend, the biological parents said they were "happy that everything went well" even though "we did not have the pleasure of holding our newborns in our arms".
But the other couple told the daily La Stampa, "We feel their pain and we are also suffering. We suggested that we all meet but they have never come back to us."