UNRWA has opened 49 of its schools to shelter those fleeing the most heavily-bombarded areas.
So far, more than 60,000 Gazans have sought sanctuary at UN institutions, the agency said.
– Hamas invited to Cairo –
Hamas “received an invitation, through mediators, for a delegation headed by Khaled Meshaal to visit Cairo and discuss the Egyptian initiative,” it said in a statement.
It said the Islamist movement said its “position on the initiative is known, but it is at the same time ready to cooperate” should its demands for a truce be met.
An Egyptian foreign ministry official said he could not confirm or deny the new invitation.
Hamas earlier in the week rejected Egypt’s proposal for a truce which was accepted by Israel saying that it had not been consulted.
Hamas relations with Egypt have hit a low since Cairo’s military regime took power last July, ousting Hamas ally the Muslim Brotherhood.
Turkey and Qatar, where Meshaal is based, are more sympathetic to the movement.
Abbas and Meshaal will meet in Qatar Sunday to discuss the Egyptian proposed truce, an official close to Abbas said.
Hamas spokesman Fawzi Barhum told AFP his movement had presented its demands to “all parties concerned, including Qatar, Turkey and the Arab League” as well as Abbas and Egypt.
The demands include a complete lift of the siege on Gaza, opening the Rafah crossing with Egypt and freedom of movement in the border areas.
In addition, Hamas demands the release of its members who had been freed in a 2011 deal and recently re-arrested in an Israeli crackdown on the West Bank.
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