CAIRO, Egypt » Egyptian mediators pushed the militant Palestinian Hamas group to accept a truce proposal for the embattled Gaza Strip in talks Tuesday, while the U.N. secretary-general headed to the region to join the multitrack diplomatic efforts for a cease-fire.

U.N. chief Ban Ki-moon has backed the Egyptian truce proposal to halt the fighting, now in its third week. Before leaving New York for the Egyptian capital on Tuesday, he urged Israel and Hamas to accept a U.N. cease-fire resolution and allow humanitarian aid into Gaza.

"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 gave its full support to Ban after he briefed the council behind closed doors ahead of his week-long trip. All 15 members gave their strong backing to the secretary-general's diplomatic mission.

Israel's point man to the cease-fire talks, Defense Ministry official Amos Gilad, is also slated to come to Cairo Thursday, Israeli Defense Ministry officials said Tuesday. Officials had initially said Gilad would travel Wednesday, then changed the day to Thursday. 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 to move closer to a cease-fire or whether to launch a new, even tougher stage of its offensive. They spoke on condition of anonymity because they were discussing sensitive policy matters.

Ban won't be meeting Hamas officials and has no plans to go to Gaza during his trip, which will also include Jordan, Israel, the Palestinian-controlled West Bank, Turkey, Lebanon, Syria and Kuwait.

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, about truce proposals.

But so far, the push has yielded little public progress. A Palestinian official close to Hamas said the previous round of Egypt-Hamas talks on Sunday were "stormy."

During that session, Egypt's top mediator, intelligence chief Omar Suleiman, told Hamas to accept Egypt's truce proposal without amendments or else Hamas will be considered responsible for Israel's continuing offensive in Gaza, the Palestinian official said, speaking on condition of anonymity for discussing the closed-door talks.

On Tuesday morning, the Hamas delegation held a new round of talks with Suleiman and Egyptian officials. Later in the day, Egyptian President Hosni Mubarak left on a previously unannounced trip to Riyadh to meet with his ally, Saudi King Abdullah to brief him on the efforts to persuade Hamas to accept an immediate cease-fire, Egyptian officials said.

Suleiman accompanied Mubarak on the trip, leaving his aides to hold further talks with Hamas on Tuesday evening, said the officials, who spoke on condition of anonymity because of the sensitivity of the talks.

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 against Israeli towns, 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.

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.

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.

Salah Bardawil, one of the Hamas negotiators in Cairo, told the Associated Press through a text message that the militant group "will not allow the Israelis to gain any political achievement from this war on Gaza."

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 a Doha summit. However, in order to call an emergency summit, at least 14 members must agree.

But Egypt and Saudi Arabia have rejected the idea, suggesting instead that Arab leaders hold talks in Kuwait on Sunday ahead of a previously planned economic summit. That proposal appeared to be aimed at preventing Qatar from taking a greater role in mediation.