Doctors in Saudi Arabia say a complex operation to separate 13-month-old Fijian conjoined twins has been successful.

In what was described as an "exceptionally rare" case, the sisters, Dicecea and Jesepeli Kikau, were born joined at the lower abdomen and pelvis.

It is a condition known as omphalo-ischiopagus tetrapus.

The girls had their own hearts and lungs and required an almost 13-hour operation to separate their liver, bowel, urinary tract and anal canal.

Loading...As the procedure reached a critical stage on Thursday night, local time, doctors announced they had successfully separated the pair and were starting on their reconstruction.

Mother Akeneta Vulimaiigiladi said she was nervous when the girls were wheeled into the operating theatre, but became less so as she watched on via a video link.

"We just kissed them goodbye and we wished our babies well,"she said.

Before the twins went into theatre, Ms Vulimaiigiladi and her husband, Watisoni, chose to give them new Arabic names: Noorah for Jesepeli and Sarah for Dicecea.

Abdullah Al Rabeeah, surgical lead at the King Abdullah Specialist Children's Hospital, told the ABC the surgery consisted of nine phases, starting with separating the liver and bowel and ending with reconstruction.

Three hours into the operation, he said it was "going well".

"Better than our expectation, and the two girls are doing well so far in spite of the complexity of surgery," Dr Al Rabeeah said.

He said separating the liver and the bowel was undertaken "with good success and stability and no major bleeding".

The operation was carried out for free under the hospital's Saudi Conjoined Twins Program.

According to the hospital, the twins were its 74th set of conjoined twins to be separated from 29 countries.

The Fijian government said the family sent the twins to Saudi Arabia after hospitals in the United States, the United Kingdom, Australia and Mexico wanted large up-front payments.

It said the offer of free treatment through the Saudi Conjoined Twins Program was a lifeline for the family.

The twins, born eight weeks premature, also have a triplet sister, Hossana, who was not conjoined.

The girls are the second recorded case of conjoined twins in Fiji in 50 years, according to the government.