Doctors are yet to identify which organs the babies share before they can be separated.
The girls, who are co-joined from the chest to the abdomen, weigh 3kg. The mother was still recovering at the hospital after she underwent a Caesarean section.
"I was expecting to deliver at Nyamache Sub-county Hospital. I don't know what happened. I have been attending my clinics regularly," said Ms Bonareri.
The woman who gave birth to her third-born said she never used any drugs or family planning method.
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"I have never used any family planning method. This is a shock to me but I believe God will get us through these challenges," she said.
John Ombogo, who carried out the Caesarean section, said the twins would be transferred to Kenyatta National Hospital for further examination.
"We have put them on oxygen but our major worry is that they might be sharing major body organs including the liver, heart and lungs," said Dr Ombogo.
Ombogo explained that the mother had abnormal presentation with three fetal limbs from the birth canal.
"This is a delicate balance that needs critical examination. We have no capacity to carry out such an operation right here in our hospital," he said.
The father of the conjoined twins, Caleb Osoro, a motorbike operator in Nyamache, called for support from well wishers.
"I have no finances to support my children go for the operation. I am saddened about the turn of events but I thank God for the far we have come," said Mr Osoro.
Dr Kelving Nyamongo, who was at the nursery unit at the time of the interview, explained that one of the babies had the larger part of the shared organs.
"These are rare cases which happen in one out of seven births. This can be caused by either use of some fungal drugs at early stages of pregnancy or chromosal issues," said Ombogo.