Sisi warned against the danger of an Israeli incursion into the city of Rafah, where an estimated 1.5 million people have sought shelter next to Gaza's border with Egypt.
Aid officials have warned of looming famine in the coastal enclave.
"We are talking about reaching a cease-fire in Gaza, meaning a truce, providing the biggest quantity of aid," Sisi said in a message recorded during a visit to the police academy.
This would include "curbing the impact of this famine on people, and also allowing for the people in the center and the south to move towards the north, with a very strong warning against incursion into Rafah", the Egyptian leader added.
Egypt "warned of what is happening, that aid not entering would lead to famine," Sisi said.
The North African nation, which fears the displacement of Palestinians crowded near its border, has been trying, along with Qatar and the United States, to mediate between Israel and Hamas to reach an agreement for a cease-fire and the release of Israeli hostages in return for Palestinian prisoners.
On Thursday, Egypt's foreign minister called on Israel to open land crossings with Gaza to let in more aid.
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