Lobna al-Saik, the baby's mother, was one of a few parents accompanying some of the 28 infants as they were taken in a convoy of ambulances from a hospital in southern Gaza, through the Rafah border crossing, into Egypt to receive treatment.
"They are innocent children, premature babies," an exhausted al-Saik said in a video interview provided by the Egyptian government. "My message to the world is 'enough'."
Egyptian television footage showed medical staff at Rafah carefully picking up tiny babies from inside Palestinian ambulances and placing them in mobile incubators, which were then wheeled across a car park towards Egyptian ambulances.
The babies, from a total of 31 moved on Sunday from the besieged Al Shifa Hospital in Gaza City to a maternity hospital in Rafah, wore only nappies and tiny green hats. They were taken to Egyptian hospitals.
"Of those 31, 11 or 12 are critically ill, all the others seriously ill," said Dr. Rick Brennan of the World Health Organisation (WHO), in an interview with Reuters in Cairo.
"Each of them has serious infections and quite a few of them have a low body temperature and so they really do need detailed specialist care," he said.
The newborns have captured global attention since images emerged eight days ago of them lying side by side on beds at Al Shifa Hospital after their incubators were switched off for lack of power amid Israel's military assault on Gaza City.
When doctors at Al Shifa raised the alarm about them, there were 39 babies. Since then, eight have died.
The story of al-Saik and her unnamed daughter provided some of the first personal details to emerge about the infants.
Al-Saik said just before the war started her baby had been receiving oxygen at Al Shifa because of breathing difficulties after her premature birth.
The family left their home on the third day of the war to escape Israeli bombardment. Like hundreds of thousands of others, al-Saik moved to the south of the Gaza Strip with her three other children, while the baby girl stayed at Al Shifa.
FAMILY TORN APART
With shortages of electricity, water, medicines and other basics, conditions at Al Shifa deteriorated and the baby lost weight and got sick.
"There was no milk and she kept getting worse, she was back to zero, to living on oxygen again," said al-Saik.
The mother was reunited with her baby in Rafah, but to accompany her to Egypt, she said she had to leave her other children behind in Gaza.
"I didn't even get a chance to hug them because I couldn't leave my daughter in this state. I didn't say goodbye to them. Something might happen to them, they could be bombed or martyred," she said, her voice breaking as tears welled up.
Jeremy Hopkins, head of UNICEF in Cairo, told Reuters the agency was working with Egyptian authorities to find out the circumstances of each of the babies, including those who did not have relatives with them, so they could be provided with support beyond the immediate medical care.
Dr Mohammad Salama, head of the neonatal unit at the Al-Helal Al-Emairati Maternity Hospital in Rafah where the babies spent Sunday night after arriving from Al Shifa, said the three who had remained behind were in a stable condition.
He said all 31 babies had been in a "catastrophic condition" when they arrived from Al Shifa and the hospital in Rafah had worked hard to stabilise them before their evacuation.
"Some were suffering from malnutrition, others from dehydration and some from low temperatures," he told Reuters by telephone.
Salama said some of the babies were with their mothers, while others were accompanied by medical staff.
The war was triggered by fighters from Hamas who rampaged through southern Israel on October 7, killing 1200 Israelis, including children and babies, and abducting 240, according to Israeli figures.
Israel has responded with a relentless bombardment of Gaza and a ground invasion.
At least 13,000 Palestinians, including 5500 children, have been killed, according to health officials in the Hamas-controlled enclave of 2.3 million people.
Three-quarters of Gazans have been made homeless by the war, according to United Nations figures.