Qatar says it has identified the parents of an infant girl dumped in a bathroom rubbish at its airport.

There have been weeks of investigation - including the physical examinations of women passengers on the day of the child's discovery that threatened to spark an international incident with Australia and other countries.

The public prosecutor's office now says it has filed criminal charges against a number of police officers at Hamad International Airport in Doha after the women passengers said they were ordered to remove their underwear for vaginal examinations.

The women said they were given no information by airport authorities and that they didn't have an opportunity to provide informed consent.

According to the public prosecutor, the infant's mother, identified as having "the nationality of an Asian country," had told the father that she had abandoned the baby in the rubbish in the departures lounge toilet before boarding a plane.

The newborn's father admitted he had a relationship with the mother and that she had sent him a message and a picture of the infant right immediately after the birth, Al-Jazeera News reports. A DNA test confirmed that the man was the child's father, other reports added.

The airport incident sparked international anger after some of the women passengers bound for Sydney - including citizens of Australia, New Zealand and Britain - complained about the extreme humiliation they had been subjected to -allegedly for evidence if they had recently given birth.

The airport police officers might face penalties of three years in prison, the public prosecutor said.

Australia Prime Minister Scott Morrison said the women's ordeal was shocking and human rights advocates asserted such forms of search were sexual assault.

Qatar's Prime Minister sheikh Khalid Khalifa bin Abdulaziz al-Thani said standard procedures were violated and that he was deeply sorry for what happened.

The newborn's mother faces charges of attempted murder, the public prosecutor said. There are international efforts to arrest "the fugitive convict" who faces a maximum penalty of 15 years in prison. It wasn't clear what charges the father faced.

The Qatar government says the infant was given full medical and social care.