Egyptian TV has shown a Palestinian Red Cross ambulance driving up to the border crossing and unloading several children on stretchers who were transferred to ambulances on the Egyptian side. About 60 relatives are also following the children to Egypt.
This is the first time in nine months that the border crossing has been opened.
Saturday's evacuation is intended to be the first in what is to become regular evacuations of Palestinians who are to be taken for medical care abroad.
During the 15 months that the war between Israel and Hamas has been ongoing, healthcare in Gaza has been severely affected and most hospitals in the area can no longer operate.
Mohammed Zaquot, who is the hospital manager within Gaza's health authority, says that more than 6,000 patients are ready to be evacuated abroad and that more than 12,000 are in urgent need of care.
The opening of the border crossing is part of the ceasefire agreement between Hamas and Israel. Israel agreed to open the crossing when Hamas released all women who were being held hostage and were still alive.
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