Egypt's President Mohamed Morsi said his government was in touch with both Israelis and Palestinians and there were indications they could "soon" reach a truce, but there were no guarantees.
"There are some indications that there could be a ceasefire soon," Morsi said at a joint news conference with Turkish Prime Minister Recep Tayyip Erdogan on Saturday adding that there were still "no guarantees."
He said his country's government was in "vigorous" communications with both the Palestinians and Israel.
A senior Hamas official had earlier said his movement was reluctant to agree a truce because it doubted the terms of the ceasefire could be guaranteed.
The Palestinian Information Centre, a website close to Hamas and acts as a mouthpiece, reported that Meshaal demanded "international guarantees" in his meeting with Egypt's intelligence chief.
One of his demands was that Israel lift the blockade it imposed on Gaza after the Islamist movement seized the enclave in 2007.
Hamas had made a similar demand to agree a ceasefire after its December 2008-January 2009 war with Israel, but the restrictions have remained largely in place.
Israel strikes on Gaza kill 14
Israeli air strikes on Gaza have killed 14 Palestinians and destroyed the Hamas government headquarters, prompting Arab leaders to call for a review of their entire policy on the Middle East peace process.
Medics said 44 Gazans have been killed and more than 390 wounded since Israel launched its aerial campaign on Wednesday afternoon, with at least eight militants among the 14 people killed on Saturday.
As the toll rose, sirens sounded in Tel Aviv for a third day, sending people scuttling for cover a day after a rocket hit the sea near the city centre, AFP correspondents said.
Israeli officials said one rocket was intercepted by the Iron Dome anti-missile system while a second hit somewhere in the Tel Aviv metropolitan area. The attack was claimed by Hamas's armed wing.
Nine people in Israel were injured by militant rocket fire.
Warplanes carried out 180 air strikes on Gaza overnight, Israeli television reported, with attacks levelling the headquarters of the Hamas government.
In Egypt, Turkish Prime Minister Recep Tayyip Erdogan said Israel would be held to account for the children killed.
"Everyone must know that sooner or later there will be a holding to account for the massacre of these innocent children killed inhumanely in Gaza," he said in a speech in Cairo.
So far, six children have been killed, the Palestinian Centre for Human Rights said.
Both Turkey and Egypt have publicly shrugged off US bids to get them to exert pressure on the Islamist Hamas into ending rocket fire, instead blaming the Jewish state for the violence.
Arabs demand review
Arab foreign ministers at an emergency meeting in Cairo roundly denounced Israel's Gaza campaign and demanded a review of what they called their futile diplomacy towards the Jewish state.
Member states should "reconsider all past Arab initiatives on the peace process and review their stance on the process as a whole", said Arab League chief Nabil al-Arabi.
In 2002, Arab states offered Israel diplomatic recognition in return for its withdrawal from all occupied territory and an equitable settlement of the Palestinian refugee question, a cornerstone of Arab diplomacy ever since.
Hamas chief Khaled Meshaal was also in Cairo on Saturday to meet Egypt's intelligence chief, Erdogan and Qatari emir Sheikh Hamad bin Khalifa al-Thani, a senior Hamas official said.
US deputy national security adviser Ben Rhodes said both President Barack Obama and Israeli Prime Minister Benjamin Netanyahu agree that de-escalation is preferable, provided that Hamas ceases firing on Israel.
"We believe that the precipitating factor for the conflict was the rocket fire coming out of Gaza," Rhodes told reporters aboard Air Force One.
"We believe that Israel has a right to defend itself, and they'll make their own decisions about the tactics that they use in that regard."
Since the start of Operation Pillar of Defence, the Israeli army says militants have fired more than 600 rockets over the border, of which 430 hit and 245 were intercepted by Iron Dome missiles.
Over the same period, three Israelis have been killed and 18 injured, including 10 soldiers, with the army saying the air force had hit more than 950 targets in Gaza.
The Israeli military in a statement on Saturday said the air force had targeted "a senior Hamas operative in charge of the terror organisation's smuggling operations ... and the senior member of Hamas's air defence unit, Mohammed Kaleb".
Four Israeli soldiers and five civilians were hurt in separate rocket attacks on Saturday, police and the army said. Hamas claimed the attack on the soldiers, while Islamic Jihad said it fired rockets which injured civilians in Ashdod.
Multiple Israeli air strikes on Gaza on Saturday killed 14 people, including at least eight militants.