"To both sides, I say: Just stop, now," Ban told a news conference Monday. "Too many people have died." He said Hamas militants who have been firing rockets into southern Israel "must stop, they must look to the future of the Palestinian people."
The U.N. Security Council on Tuesday unanimously supported Ban's efforts after he briefed the council behind closed doors.
Tuesday's talks between Hamas and Egyptian officials in Cairo were the latest in intensive diplomatic efforts. In Damascus, the Turkish prime minister's top foreign policy adviser, Ahmet Davutoglu, met for the third time in two days with Hamas' exiled political leader, Khaled Mashaal.
But so far, the push has yielded little public progress.
Hamas' deputy leader Moussa Abu Marzouk told Al-Jazeera TV that the Egyptian proposal is not acceptable as it stands. Hamas has "amendments" for it and if "taken into consideration, it will be a framework for moving toward a solution," he said.
One Egyptian official on Tuesday accused Hamas of procrastinating and making preconditions. "They want to score a political victory, regardless of how long this bloodshed will continue," the official told The Associated Press, speaking on condition of anonymity because the talks are closed.
A Palestinian official close to Hamas said the previous round of Egypt-Hamas talks on Sunday were "stormy." The official spoke on condition of anonymity because he was discussing closed-door talks.
Israel's point man to the cease-fire talks, Defense Ministry official Amos Gilad, is slated to come to Cairo Thursday, Israeli Defense Ministry officials said Tuesday. Gilad had put off the trip for days, saying the time was not yet ripe.
Defense officials say that depending on what happens in Cairo, Israel will decide whether to move closer to a cease-fire or launch a new, even tougher stage of its offensive. They spoke on condition of anonymity because they were discussing sensitive policy matters.
During the Sunday negotiating session, Egypt's top mediator, intelligence chief Omar Suleiman, told Hamas to accept Egypt's truce proposal without amendments or Hamas will be considered responsible for Israel's continuing offensive in Gaza, the Palestinian official said.
On Tuesday, the Hamas delegation held a new round of talks with Suleiman and Egyptian officials. Later, Egyptian President Hosni Mubarak left on a previously unannounced trip to Riyadh to meet with his ally, Saudi King Abdullah, to discuss the cease-fire efforts, Egyptian officials said.
The talks come as Israeli ground troops pushed deeper into Gaza City in their 18-day offensive, in which more than 900 Palestinians have been killed, half of them civilians. Israel says its assault aims to stop Hamas rocket attacks, saying it will stop only when there are guarantees the rocket fire and smuggling of weapons into Gaza will stop.
Hamas demands an immediate withdrawal of Israeli forces from Gaza, a halt to the offensive and the opening of border crossings into the tiny Mediterranean coastal territory, which Israel and Egypt have mostly kept sealed since Hamas took power in Gaza in 2007.
How those crossings are to be opened, however, is a major sticking point. Egypt has called for international monitors at the borders to prevent smuggling, although not on the Egyptian side of the border, and there is also talk of such monitors being tasked with ensuring the cease-fire. Hamas has so far rejected any international monitors and demands a role in controlling the border crossings, which Egypt and Israel refuse.
Qatar has called for an emergency summit of Arab League heads of state on Friday in Doha to discuss the Gaza crisis.
Arab League head Amr Moussa said 13 members have agreed to attend. However, at least 14 members must agree for a summit to be called.
Egypt and Saudi Arabia have rejected the idea, suggesting Arab leaders hold talks in Kuwait on Sunday ahead of a previously planned economic summit.
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