Hamas and Israel have signaled that both are looking to end a flare-up in violence that began four days ago.
Ghazi Hamad, Hamas’ deputy foreign minister, delivered a rare appeal to the Israeli public on Sunday, calling for a halt to the escalating cross-border fighting.
Speaking in Hebrew to state-run Israel radio, Hamad said: "We are interested in calm but want the Israeli military to stop its operations."
Also speaking to Israel radio, Ehud Barak, the Israeli foreign minister, said Hamas had been hit hard in the past few days and a ceasefire may be the way to go.
"If they stop firing on our communities, we will stop firing. If they stop firing in general, it will be quiet, it will be good," Barak said.
The cross-border violence erupted on Thursday after Palestinian fighters fired an anti-tank missile at a school bus, critically wounding a teenager and injuring the driver.
Israel has since then launched a series of air raids at targets throughout the Gaza Strip, killing 19 Palestinians, both fighters and civilians.
Nicole Johnston, Al Jazeera correspondent in Gaza, said that "civilians have paid a very heavy price, not only are they being killed but also dozens have been injured".
"Most of the injured are children … there were children aged between 10 and 15 years, playing football, when a rocket hit and they were injured by pieces of shrapnel."
Armed fighters from Gaza have fired at least 120 rockets and mortars at southern Israel during the conflict, with rocket fire continuing on Sunday, according to the Israeli army.
A number of rockets have been shot down mid-air by Israel’s newly deployed Iron Dome interceptor.
Binyamin Netanyahu, the Israeli prime minister, said Israel would raise the stakes if cross-border attacks continued.
"Our policy is clear, if the attacks continue on Israel’s citizens and soldiers, the response will be much harsher," Netanyahu said at the start of a weekly cabinet meeting.
Also on Sunday, Amr Moussa, the Arab League chief, said that the organisation would ask the UN Security Council to impose a no-fly zone over Gaza following the Israeli air raids.
The UN and European Union have both called for an end to the cross-border violence.
Israel Radio said Robert Serry, the UN Middle East envoy, was trying to mediate a halt to the violence, and the Egyptian state news agency said Egypt was engaged in similar efforts.
Some political analysts have explained the recent cross-border escalation as an effort by Hamas to divert attention from demands, fuelled by pro-democracy unrest in the Arab world, for an end to the group’s split with Fatah.
The Western-backed Fatah movement controls the West Bank after Hamas seized control of the Gaza Strip in 2007.
(Al Jazeera and Agencies)