Qatar said Monday it had identified the parents of a baby girl dumped at its airport, an incident that prompted officials to order departing female passengers to undergo invasive examinations, sparking global outrage.

The public prosecutor said the mother and father were from "Asian countries" which in Qatar typically refers to the nations of South Asia where a large number of migrant workers come from.

Efforts were under way "to arrest the fugitive" who is overseas and faces 15 years imprisonment, the prosecutor said in a statement that called her a "convict", suggesting she may have been convicted in absentia.

Women on 10 Qatar Airways flights out of Doha, including one to Sydney, were subjected to the examinations following the incident on October 2, leading to a diplomatic row with Australia.

"Investigations revealed that the infant's mother... threw the newborn infant in the trash can in one of the toilets in the departures lounge at the airport and boarded the plane to her destination," the prosecutor said.

"(The mother) had a relationship with another person of the nationality of one of the Asian countries as well, and this relationship resulted in the infant that was found.

"The father of the infant admitted that he had a relationship with the infant's mother, and that she had sent him a message and a photo of the newborn infant immediately after her birth."

The mother had told the father that she had dumped the baby and departed the country, the statement added, while DNA screening proved they were the child's parents.

All expatriates coming to Qatar for long-term work are required to give a substantial sample of blood during the registration process.

'Unacceptable treatment'

Two Doha-based sources have told AFP that Qatari authorities had requested an Interpol red notice in order to have the woman identified as the mother brought to Doha to face charges.

The incident only came to light weeks after it occurred, when affected Australian passengers spoke out, with Canberra labelling the episode "appalling".

The public prosecutor said "some employees" of airport security had broken the law by ordering the searches -- for which Qatar only apologised weeks after they took place -- and face three years imprisonment.

It gave no details of how senior those charged were, or how many would be punished.

Diplomats have suggested that such a major operation requiring the suspension of flight operations at the authoritarian state's airport could not have been authorised by a handful of junior staff.

Qatar is an ultra-conservative Muslim monarchy, where sex and childbirth outside of marriage are punishable by jail.

Ahead of the 2022 World Cup in Qatar, it has struggled to reassure critics that its promises on women's rights, labour relations and democracy are credible.

Prime Minister Sheikh Khalid bin Khalifa bin Abdulaziz Al-Thani, who as interior minister is also responsible for the security services, previously tweeted that "we regret the unacceptable treatment of the female passengers" at Doha airport.