The doctors said the back-up generators did not work because of poor maintenance.
The video shows doctors trying to help the babies with Ambu bags, hand-held devices used to provide ventilation to patients who have trouble breathing.
"We had five cases that needed this. We only had two Ambu bags," the doctor interviewed by Reuters said. He said a third bag later came in from another department at the hospital.
Another doctor, who also runs the blog, said: "How come a hospital with six intensive care units relies on one source of electricity?" Both doctors spoke on condition of anonymity, fearing management retribution.
But Mortagi Negm, secretary-general of educational hospitals and institutions, a government department, said the power outage had no effect on the health of any baby at the nursery.
"Two babies died before the electricity went off," he told Reuters. "The law states that they must remain on the machine for two hours after death."
Reda Salama, the mother of 20-day-old Ali Gamal who died that night, does not believe this. She says gross negligence by the hospital led to the death of her son.
"I want those who caused the murder of my son dead. Even if I strangle them myself, it won't satisfy me," she said, sitting in a small room in her dilapidated home in Bahteam, a poor district in Cairo. She was wearing a black dress and a black headscarf as a sign of mourning.
"GREAT SYSTEM ON PAPER"
Salama, who sells fruit and vegetables on the street while her husband works at a textile factory, said she was not seeking financial compensation.
"This is negligence," she said in a loud, angry voice as she sat surrounded by relatives. "If I give up the rights of my son and others do the same, what will become of us?"
The deaths at the hospital received front-page treatment in independent and opposition newspapers. Dozens of people phoned television talk shows and sent messages to online forums attacking the government's health policies, which they blame for the run-down system.
The Ministry of Health will spend some 12 billion Egyptian pounds (1.12 billion pounds) on health care this year. In comparison, the government spends nearly 80 billion on food and fuel subsidies, and spending on defence and security will be about 22 billion pounds next year.
Health Minister Hatem el-Gabali has vowed to "chop off the heads of those responsible" if investigations prove the power outage caused the death of any infants. He acknowledged that public hospitals in Egypt were battling many problems.
"Funding is scarce," he told state-run Egyptian television in an interview. "On paper, we have a great system. On paper, the powers, obligations and rights are great."
Gabali said state-run hospitals were in reality negligent and that connections and favouritism played a role in the appointment of employees. "And who pays the price? You and the citizen," he said.
