More than two dozens babies were expected to cross, according to the Palestinian Red Crescent and Egypt’s Al Qahera TV.
The newborns had been in north Gaza’s Al Shifa hospital, where several other newborns died amid a collapse in medical services partly caused by power cuts when fuel ran out.
Israeli forces seized Al Shifa last week to search for what they said was a Hamas tunnel network built underneath.
Hundreds of patients, medical staff and displaced people evacuated Al Shifa at the weekend, with doctors saying they were ejected by troops and Israel saying the departures were voluntary.
Live footage aired by Al Qahera showed medical staff carefully lifting tiny infants from inside an ambulance and placing them in mobile incubators, which were then wheeled across a car park towards other ambulances.
The babies had been transported on Sunday to a hospital in Rafah, on the southern border of Hamas-ruled Gaza, so their condition could be stabilised ahead of transfer to Egypt.
At another hospital, funded by Indonesia, Gaza’s health ministry said at least 12 Palestinians were killed and dozens wounded by firing into the complex encircled by Israeli tanks.
There was no immediate comment from the Israeli military about the situation at the hospital where health officials said 700 patients along with staff were under fire from Israeli forces.
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The Palestinian news agency WAFA said the facility in the northeast Gaza town of Beit Lahia had been hit by artillery fire.
Palestinian health officials said there were frantic efforts to evacuate civilians out of harm’s way.
Hospital staff denied there were any armed terrorists on the premises.
Israel says its forces in Gaza are attacking “terror infrastructure” and accuse Hamas of waging war behind human shields, including in hospitals. The Islamist group denies this.
“We had information earlier that tanks were besieging the Indonesian Hospital. Unfortunately…, communications there are almost cut,” Nahed Abu Taaema, director of Nasser Hospital in the southern Gaza city of Khan Younis, told Reuters.
“We are very concerned about the fate of our colleagues and the fate of wounded and patients as well as (displaced) people who may have still (been) sheltering there. No ambulances can reach them, and we’re afraid the wounded will die,” said Abu Taeema.
Indonesia’s foreign ministry said it had lost contact with three Indonesian volunteers at the hospital who are part of the group that set up the facility in 2016 with Jakarta’s funding.
Indonesian Foreign Minister Retno Marsudi condemned what she called Israel’s “attack” on the hospital, saying it clearly violated international humanitarian laws, and urged countries close to Israel to get it to stop the violence.
Like all other health facilities in the northern half of Gaza, the Indonesian Hospital has largely ceased operations but is still sheltering patients, staff and displaced residents.
Israel has ordered the complete evacuation of the north, but thousands of civilians remain, many seeking shelter in hospitals. Fuel and medicines have been running out across the entire enclave under Israel’s six-week-old siege.
In the south, where hundreds of thousands of Gazans who fled the north of the enclave are sheltering, at least 14 Palestinians were killed in two Israeli strikes on houses in Rafah, according to Gaza health authorities. There was no immediate Israeli comment on the incident.