Beijing (CNN) -- Conjoined twin girls -- each with a fully developed skull, but sharing one body -- have been born in China, according to their father, who said the babies are suffering from a host of health problems.

"The doctor said they are in critical condition," father Liao Guojun told CNN by telephone, as his babies cried in the background in a hospital intensive care unit. "The girls suffer from more than 10 illnesses right now and their chance for survival is very low."

But he said the girls -- affectionately dubbed "Left sister" and "Right sister" by their parents -- bring the new mother and father much joy.

"They cry at the same time, they sleep at the same time and they wake up together, and sometimes their hands wiggle in the air, grabbing for each other's hand," Liao said. "It's very cute."

The babies were born May 5 in China's southwest Sichuan province, in the small city of Suining. They share one trunk, one pelvis, one spleen, one gallbladder and one reproductive system. Initial X-rays show they have two spines, two esophagi, two stomachs, two sets of lungs and two separate nervous systems.

The babies have been moved from Suining to Xin Qiao Hospital in the city of Chongqing for further examination. The hospital has classified them as "high risk," as they suffer from conditions including anemia, pneumonia, jaundice and neonatal sepsis. Liao said doctors have said they cannot rule out epilepsy or cerebral palsy.

China's state-run Xinhua news agency reported Wednesday that the babies' combined weight is about 4 kilograms (8 pounds). Xin Qiao Hospital has successfully separated four pairs of conjoined twins, according to Xinhua.

However, doctors said the twins may not need immediate separation surgery as long as they can grow in a healthy way, Xinhua reported. And Liao said doctors told him that a separation surgery would be impossible, since the babies share one-and-a-half hearts, and that the structure of their trunk is not conducive to a surgery that either child would survive.

"I am very worried," Liao said. His wife remains hospitalized in Suining as she recovers from the birth, he said, and calls constantly to hear her daughters and receive updates on their condition.

Preliminary imaging results have showed the babies' two skulls are fully developed and have normal facial features, according to state-run media.

The couple had had several health checks, beginning six months ago, and believed they were having one healthy child. At a final pregnancy examination three days before birth, doctors told the parents they were having "one baby with two heads," Liao said.

The parents did not know the sex of the babies. Scanning to determine the sex of a baby in China is illegal, a rule designed to prevent sex-selective abortions.

Liao said the parents were shocked by the news but moved forward with the birth.

Liao said he worked as a cook in Guangdong province before the babies were born, and his wife was a factory worker for a cotton clothing manufacturer before she returned to Suining.

The cost of the babies' care far outpaces the couple's modest income, so hospitals and social service organizations in Suining have stepped in to help foot the bills.

"The hospitals have never asked us for money," Liao said. "Medical experts from across China are flying in to help us."

He said he hopes the babies, along with his wife, will recover.

"The girls are different than the other children because they have two heads," he said. "Their health conditions are poor. (But) we hope that since they were born to us, in this world, that they can live their lives as they were meant to do."

CNN's Helena Hong contributed to this report.