Near the Israel-Gaza border (CNN) -- 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.
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."
Health officials in Gaza say 46 people have been killed and 440 people wounded since Israel's military operation, dubbed Pillar of Defense, began Wednesday.
Israel is reporting three deaths from a Hamas rocket attack in the southern community of Kiryat Malachi. At least 18 Israelis have been wounded, including five civilians and four Israeli soldiers wounded by rocket fire from Gaza, the military said.
For days, Israel has been using airstrikes to target what it describes as rocket-launching sites operated by Hamas and other militant groups. Israeli airstrikes have hit more more than 830 targets in Gaza since the operation began, the IDF said.
The IDF, which describes Hamas-run Gaza as a "front-line base" for its adversary, Iran, said it targeted a Hamas base in southern Gaza and two Hamas operatives on Saturday, one in charge of smuggling and an air defense official.
Palestinian militants, meanwhile, launched a barrage of rockets at southern Israel, including four that hit the coastal community of Ashdod, the IDF said. One of the rockets hit a house and another landed near a kindergarten, the IDF said. There were no immediate reports of casualties.
The Izzedine Al Qassam Brigades said its fighters shelled the Zikim military base near Ashkelon and the Israeli cities of Ashdod and Beer Sheva.
The group also claimed Saturday to have shot down an Israeli F-16 over the Mediterranean Sea. It didn't say when the downing allegedly occurred.
An IDF spokeswoman denied the claim, saying all aircraft are accounted for.
"It didn't happen and we have no record of it," said the spokeswoman, who could not be named in line with policy.
Hamas accused Israeli warplanes of hitting an apartment building Saturday in the Jabalya refugee camp in northern Gaza, killing at least three people and wounding more than 30, according to Hamas-run al Aqsa TV. Footage broadcast by al-Aqsa showed people clamoring over smoking ruins, searching for survivors.
Palestinians incensed by Israel's offensive took to the streets in the West Bank, the Palestinian territory whose government is dominated by the Fatah movement.
Four people were seriously wounded in Beitanya near Ramallah when Israeli soldiers fired "high-velocity projectiles" toward demonstrators, Palestinian medical sources said. Seven others were lightly injured by rubber steel-coated bullets and tear gas inhalation, the sources said.
In Bait Omar, demonstrators attempted to march out of the village but were stopped by Israeli soldiers, who fired stun grenades and tear gas.
Fatah and Hamas have been fierce rivals in recent years. Fatah is more moderate on Israel than Hamas, and Hamas leaders have engaged in peace talks with Israel over the years.
CNN's Sara Sidner reported from Gaza City; CNN's Fred Pleitgen reported from southern Israel; and journalist Mohamed Fadel Fahmy reported from Cairo. CNN's Kindah Shair reported from Jerusalem; CNN's Chelsea J. Carter, Joe Sterling and Yousuf Basil reported from Atlanta. CNN's Jessica Yellin, Ben Wedeman, Amir Ahmed and Joe Vaccarello and journalist Per Nyberg contributed to this report.