Ali and Sara, born in Islamic State's self-styled caliphate in northern Iraq, escaped to a camp for displaced people only to confront a new challenge -- with no identity documents, they risk joining a generation of stateless children.

After seizing large parts of Iraq and neighbouring Syria in 2014, Islamic State group imposed its strict interpretation of Islamic law and began to establish the basic frameworks of statehood such as taxes and regulation.

But that project is collapsing in the face of a military campaign in Iraq to crush the militants, with unexpected consequences for ordinary people escaping their grip.

Births in Islamic State-controlled areas were registered with authorities that are not considered valid outside that shrinking territory - or not registered at all.

That is adding hundreds and perhaps thousands of children under the age of 2-1/2 to the growing numbers of children across the Middle East who are stateless - lacking legal recognition as a citizen of any country.

Stateless children risk missing out on basic rights such as education and healthcare, are likely to face difficulties in adulthood getting a job, and are exposed to abuse and trafficking, according to the United Nations.

The five-year-old civil war in neighbouring Syria, which has uprooted 10 million people, threatens an even greater number of children born in areas outside Syrian government control or in refugee camps beyond its borders.

Sara was born just as the ultra-hardline Islamists stormed across Iraq in 2014. Her little brother Ali was born two years later, days before his family fled to Debaga camp from their village south of Mosul, Islamic State's last major stronghold which Iraqi forces are now battling to retake.

The children's father, Mohamed, says he did not register either birth with Islamic State.

"If you brought them a child, they would issue a birth certificate themselves in the name of their state," he said, spurning that proposition.

Some parents did register their newborns with Islamic State group, which issued proprietary birth certificates bearing the group's black-and-white logo declaring "There is no god but God".

Furaq, a 22-year-old from the Mosul area, showed Reuters a lightweight pink document issued by the group when his eight-month-old son Yasser was born. It closely resembles its Iraqi equivalent.

Mahdi Waili, head of the government directorate which deals with nationality, said parents whose children do not have birth certificates would be able to go to the health ministry offices to arrange for their births to be registered.

However, months after some areas in northern Iraq were retaken from Islamic State group, local government services have yet to be reinstated.

Other parents privately say they obtained Islamic State documents for their children but tore them up when Iraqi forces pushed out the militants, fearing reprisals for what could be seen as cooperating with the group.

Ali, a first-time father from inside Mosul, spoke to Reuters last week holding his 19-month-old daughter Amal, who was born with a brain defect that has kept her from learning to walk.

He secured a birth certificate for the girl from a neighbour who worked in the local hospital but refused to let Islamic State authenticate it with their official stamp.

"The doctor told me, 'Don't let anyone know you have the certificate or they will slaughter us both'," Ali said.

Abu Saud, 41-year-old father of five, said he decided not to register his son's birth in October 2014 at a village south of Mosul controlled at the time by Islamic State.

"With my other children, I would go to the residency department to register them with a photo and stamp," he said outside his tent in Debaga. "It proves that this is my child or your child or his child. But now, he doesn't have an ID card."

The United Nations refugee agency UNHCR says it wants Iraqi authorities to issue birth certificates for children born in areas controlled by Islamic State.

Debaga camp manager Ahmed Abdo said his staff is working with the United Nations, a Swedish NGO and the Iraqi government to try to resolve the problem, and so far UNHCR has provided legal assistance to help resolve 175 cases.

But a UNHCR spokesman said a significant increase was anticipated as the roughly 1.5 million people still living inside Mosul emerge from Islamic State rule.

Belkis Wille, Iraq researcher for Human Rights Watch, said Iraqi authorities have an international legal obligation to grant nationality to all people born stateless in their territory.

"They should make it a priority to allow these families to reintegrate and get access to school and benefits for their children as quickly as possible," she said.