According to sources, the five children were being treated for various ailments including breathing problems and were put on ventilators and incubators at the hospital in the Korangi area of Karachi.
"The oxygen supply to the incubators ended and no one was there to refill or do something. Five infants died because of this," said Manzoor Ahmed, the father of one of the infants.
He claimed that two infants had died in a similar fashion at the same hospital a week ago and even though the parents protested and lodged complaints nothing was done to redress them.
The Sindh governor has set up a three-member inquiry committee of the health department to probe the matter.
Pakistan has been plagued by a chronic power crisis in recent years.