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Israel has also authorised the call-up of 75,000 military reservists, so far mobilising around half that number.
The Gaza fighting has stoked the worries of world powers watching an already combustible region.
In the absence of any prospect of permanent peace between Israel and Hamas and other Islamist factions, mediated deals for each to hold fire unilaterally have been the only formula for stemming bloodshed in the past. But both sides now placed the onus on the other.
Izzat Risheq, aide to Hamas politburo chief Khaled Meshaal, wrote on Facebook that Hamas would enter a truce only after Israel “stops its aggression, ends its policy of targeted assassinations and lifts the blockade of Gaza”.
Listing Israel’s terms, Vice Prime Minister Moshe Yaalon wrote on Twitter: “If there is quiet in the south and no rockets and missiles are fired at Israel’s citizens, nor terrorist attacks engineered from the Gaza Strip, we will not attack.”
Yaalon also said Israel wanted an end to Gaza guerrilla activity in the neighbouring Egyptian Sinai, a desert peninsula where lawlessness has spread during Cairo’s political crises.
Israel bombed some 80 sites in Gaza overnight, the military said, adding in a statement that targets included “underground rocket launching sites, terror tunnels and training bases” as well as “buildings owned by senior terrorist operatives”.
Netanyahu has said he had assured world leaders that Israel was doing its utmost to avoid causing civilian casualties in Gaza. At least 22 of the Gaza fatalities have been children, medical officials said.
Before leaving for Cairo, Ban urged Israel and the Palestinians to cooperate with all Egyptian-led efforts to reach an immediate ceasefire.