The Pakistan Institute of Medical Sciences in Islamabad housed at least 15 newborns in the nursery and at least one baby was rescued from the fire that began about 6.45am on Wednesday after an air-conditioning unit compressor exploded inside the nursery on the third floor.
The fire was confined to the nursery in the gynaecology ward, while the rest of the hospital remained unaffected and there were no other injuries reported, according to hospital officials and witnesses.
Television footage showed rescue workers using ladders to reach the area through broken windows.
"One baby was rescued by a doctor," said Dr Aneeza Jalil, a hospital spokeswoman.
She said the bodies of six babies had been handed over to their families, while the remaining bodies would be released soon.
The death toll of 14 children was confirmed by federal Health Minister Mustafa Kamal, who oversees the nation's health ministry under Prime Minister Shehbaz Sharif.
Hours later, Sharif ordered health secretary Aslam Ghauri, the ministry's highest civil servant, to be removed from office.
Officials were in contact with the families, according to Kamal, who said the immediate priority was to support the parents and return the infants' bodies to them.
The deaths of the children sent a wave of shock and grief across the country.
Police were deployed at the hospital as grieving parents and relatives gathered, some weeping while others called for accountability and demanded answers about how the fire began and whether the nursery had adequate firefighting equipment.
A woman who identified herself as Mrs Mohammad Sami said she gave birth three days earlier and her baby was receiving intensive care in the nursery when the fire erupted.
She said hospital officials told families that the bodies would be released after the necessary paperwork was completed.
"I don't know what to say or whom to blame," she said through tears. "I have lost my child.
Firefighters quickly responded and extinguished the blaze and rescue teams began cooling operations at the site, local media reported.
Islamabad Chief Commissioner Suhail Ashraf later said the fire had been extinguished and authorities were co-ordinating with the families.
Wednesday's fire was among Pakistan's deadliest recent tragedies involving children.
In June, 14 schoolchildren were killed and eight others injured when the roof of a tutoring centre under construction collapsed in the eastern city of Lahore.
Within hours, the Islamabad district magistrate appointed a multi-agency fact-finding committee with directions to submit a report within 24 hours.
The panel will investigate the cause of the fire and its spread, determine whether adequate fire-safety measures were in place and evaluate the emergency response, a government notification said.
Interior Minister Mohsin Naqvi and Sharif expressed sorrow over the fire.
"A tragedy involving children is an irreparable loss," said Sharif, who ordered an immediate investigation.
Sharif held a high-level meeting within hours where he removed Ghauri and expressed anger at other officials from relevant agencies in attendance, according to a government statement.
President Asif Ali Zardari also offered condolences to the families, describing the deaths as "heartbreaking and an irreparable loss".
Zardari called for those responsible to be identified and dealt with under the law and urged hospitals to ensure effective fire-safety measures and emergency procedures, particularly in wards caring for newborns.
