Three of the ten babies who died have yet to be identified, leaving some parents unsure about what happened to their children.
Santoshi, a new mother, is still looking for her 10-day-old baby.
“When the fire broke out, I couldn’t go inside to rescue my baby. How could I? When no one was able to get inside, how could anyone hand me my baby?” she told ANI news agency.
The blaze on Friday night at Maharani Laxmi Bai Medical College Hospital is being blamed on an electrical fault.
Pictures from the scene showed anguished parents outside the hospital.
Indian media reported that the fire first sparked in the intensive care unit of the infants’ ward at around 22:30 local time (17:00 GMT).
Local officials believe an electrical short circuit or another fault in a machine used to increase the level of oxygen in the ward caused the fire.
Indian Prime Minister Narendra Modi posted a message online calling the deaths “heart-wrenching”.
“My deepest condolences to those who have lost their innocent children in this. I pray to God to give them the strength to bear this immense loss,” he wrote.
Officials from the Uttar Pradesh state government have announced compensation of 500,000 rupees (£4,600; $5,900) for the bereaved families.
State deputy chief minister Brajesh Pathak said a safety review of the public hospital had been carried out in February, and a fire drill as recently as June.
This is the second prominent hospital fire in India in six months where newborns have been killed. In May, six babies were killed in a fire at a private neonatal facility in Delhi.