Egypt's intelligence chief is spearheading talks with Hamas and Israel to forge a stop to the five days of warring that has engulfed Gaza and the Jewish state and head off an Israeli ground offensive into the besieged Palestinian territory.
Mohammed Shehata contacted Israel and requested that it "calm down" the situation, a general with Egyptian intelligence told CNN. He is trying to persuade both sides to reach a cease-fire, and negotiations are still ongoing with no clear conclusion yet, said the general, who asked not to be named.
The Palestinian Information Center, a Hamas-run media outlet, said Shehata met with Hamas leader Khalid Meshaal on Saturday in an attempt "to calm the situation and stop the Zionist assault on Gaza."
Meeting in the Egyptian capital of Cairo, Meshaal's delegation passed along conditions for a process that would ease the situation and reach an agreement.
It wants a halt to "all acts of aggression and assassination" from Israel and a lifting of Israel's blockade on Gaza in exchange "for stopping the rockets" targeting Israeli cities, the center said.
The center cited sources from the Hamas delegation in Cairo, saying the movement has received a number of requests through European mediators to stop the fighting.
As Palestinian fighters and Israeli soldiers traded fire, Israeli troops and tanks massed near the border of the Palestinian territory Saturday, hinting at an imminent ground invasion.
Convoys carrying tens of thousands of Israeli soldiers rolled toward Gaza, part of what the IDF described as the mobilization of 30,000 troops along the border with Israel.
The Israeli government has authorized calling up 75,000 reservists.
"Israel will take all necessary and legitimate measures to defend its citizens, including ground operations," Israeli's ambassador to the United States, Michael Oren, told CNN.
There was no immediate word from Israel about the initiatives to end its days-old military campaign aimed at stopping daily rocket attacks from Gaza.
Rockets soared from Gaza toward Israel all day Saturday, including one that was blocked by a missile defense system as it headed straight to Tel Aviv.
Hamas' military wing, the Izzedine Al Qassam Brigades, said Saturday it has fired more than 900 rockets at Israel since the fighting began. A spokesman for the Israel Defense Forces put the number at 1,000.
Air raid sirens screamed in Tel Aviv, and Hamas' military wing claimed responsibility for shelling the city. But the IDF said its Iron Dome missile defense system blocked the Tel Aviv-bound rocket.
Q&A: Gaza strikes could be beginning of ground attack
Earlier Saturday, Israeli warplanes leveled the Palestinian Cabinet building, where Egyptian Prime Minister Hesham Kandil met Friday with Hamas officials. The strikes hit the office of Prime Minister Ismail Haniyeh, the Hamas Ministry of the Interior and a police compound, Israel and Hamas said.
Rockets fell Friday near Jerusalem, Israel's seat of power.
Leaders across the world have called on Israeli and Palestinian governing bodies to show restraint, fearing at a minimum a possible repeat of Israel's 2008 invasion that left at least 1,400 people dead.
Arab League foreign ministers met in an emergency session in the Egyptian capital, and the group's secretary-general, Nabil Elaraby, denounced Israeli actions, echoing the criticism of Israel from other leaders across the Middle East and Muslim world.
Elaraby said the Arab League should reevaluate and question the benefits the Middle East peace process -- which he called "a process without peace." And, he said, the Arab nations should work to bring the issue front and center to the international community.
A White House spokesman, saying "the precipitating factor" for the current conflict was the rocket fire from Gaza into civilian areas, stressed that "Israel has a right to defend itself." He also underscored the importance of Israel avoiding civilian casualties.
Oren said Israel regrets any loss of civilian life in Gaza, but said Israel is simply trying to send a message to Hamas that it cannot kill Israeli civilians with impunity.
Hamas, Oren said, is "a genocidal organization" that does not accept Israel's legitimacy and is not looking to negotiate with Israel.
Israel wants peace and is willing to negotiate with its neighbors, if they are willing to do the same, the ambassador said.
"Everything's on the table. We sign on to the two-state solution," Oren told CNN. "We're committed to it. Just stop shooting at us."