GAZA CITY (CNN) -- With an Egyptian official acting as an intermediary, Hamas on Monday gave Israel its conditions for a cease-fire, a general in Egyptian intelligence told CNN.
A special Israeli delegation received the letter in Cairo from intelligence chief Mohamed Shehata, the general said.
"We are optimistic about the negotiations so far," the general said.
No details of the conditions were immediately available, nor was there any immediate confirmation of the letter from Israel.
The movement comes amid mounting international pressure to end the hostilities, including U.N. Secretary-General Ban Ki-moon flying to the region to personally appeal for a cease-fire.
Ban's call for a truce came on the heels of the single deadliest attack -- an Israeli airstrike that killed a family of 10 -- in the conflict that began with militant rocket attacks from Gaza, to which Israel responded with an aerial offensive.
"This must stop," Ban said late Sunday. He called on both sides to cooperate with Egyptian-led effort to broker a cease-fire.
"I am heading to the region to appeal personally for ending the violence and contribute to ongoing efforts to that end," he said.
Ban joins a growing chorus of Western and Arab diplomats calling for end to the crisis that has raised fears of a repeat of Israel's 2008 invasion of Gaza following a similar spate of rocket attacks. At least 1,400 people were killed in that conflict.
In Israel, three people have been killed and 68 wounded in rocket attacks, the Israel Defense Forces says.
At least 92 people have been killed in Gaza since Israel began its aerial campaign, Palestinian emergency services said Monday. About 750 people in Gaza have been injured, the group said.
Neighbors and family members used a ditch digger, shovels and, in some cases, their hands to dig through the debris of a two-story house blown apart by an Israeli airstrike.
Ten members of one family were buried in the broken concrete and mangled metal, relatives told CNN.
A ditch digger was used to lift a giant slab of concrete. Underneath, the bodies of two small children were discovered.
Nearby, men dug through concrete blocks to find a missing woman.
"She's my uncle's wife," a young man shouted as he tried to get to a debris pile where the woman was believed buried. "She lived here."
A short time later, the body of the elderly woman was uncovered.
On Twitter, the al Qassam Brigades -- Hamas' military arm -- called it a "massacre committed by Israeli occupation."
The Israeli airstrike was targeting Yehya Bayaa, "a senior Hamas member," said Lt. Col. Avital Leibovich, the IDF's chief spokeswoman. The IDF alleges Bayaa is one of the leaders of a Hamas rocket-launching unit.
"When I say a senior Hamas member, I mean members that have Israeli blood on their hands -- members of Hamas that planned either the abduction of soldiers or are very much involved in targeting Israelis," Leibovich said.
The house was Bayaa's home and suspected command center, according to Leibovitch. She said the Israeli military was examining video of the strike to look for signs of secondary explosions, an indication that there were explosives inside. Initially, the IDF reported it killed Bayaa in the attack. But late Sunday, Leibovich said she did not know for sure whether Bayaa had been killed.
Rockets flew overhead as mourners gathered Monday at the al-Isra mosque for the funeral of some of the family members killed, CNN's Ben Wedeman reported. A short time later, the sound of the firing of more rockets could be heard.
Hundreds turned out for the funeral, where some chanted, "revenge, revenge."
Also on Monday, militants fired six rockets toward Eshkol in southern Israel, with one hitting a school that has been shuttered since the conflict began, the IDF said. Three more rockets fired at Ashkelon -- which has been repeatedly targeted by militants in recent days -- were intercepted by Israel's missile defense system, it said.
Airstrikes Monday in Gaza targeted a stadium where the IDF alleges Hamas militants were launching rockets.
Overnight, a fairly intense air campaign was carried out with a number of airstrikes targeting primarily government buildings.
In the daylight, Gaza City looked something like a war zone with flattened buildings, emptied streets and shuttered store fronts.
An Israeli special envoy was in Egypt for cease-fire talks Monday, the Egyptian government said, and a steady stream of Arab League, U.N. and European diplomats were arriving in the region to promote a cease-fire.
Hamas is putting conditions on any truce offer. In addition to an end the airstrikes, senior Palestinian negotiator Nabil Shaath said Hamas is demanding the end to Israel's long blockade of Gaza.
The territory has been under a crippling economic embargo since Hamas won control of the territory from the Fatah-led Palestinian Authority, which controls the West Bank.
Hamas also wants Israel to stop targeting the leadership of Palestinian factions and to expand the waters Palestinian fishermen are allowed to trawl from three miles offshore to 30, said Shaath, who is also a Fatah leader.
"The attempt is to reach a real stable situation. That's why they are asking for commitment on Israeli typical aggression and periodic incursions and constant shooting and firing at the fishermen in the sea," he said.
Israel, meanwhile, has demanded an end to the rocket attacks.
Militants in Gaza had fired nearly 1,000 rockets at Israel, the IDF reported. Roughly 550 rockets have struck Israel and another 340 have been intercepted, including 41 of the 146 fired Sunday, the military said. About 110 rockets fires by militants in Gaza have landed inside the Palestinian territory.
Israel, meanwhile, carried out 130 strikes during the day, raising to 1,350 the number of sites targeted since it began its bombing campaign on Wednesday, according to the IDF.
The IDF has struck government buildings, police stations and the homes of Hamas officials as well as rocket-launching sites and suspected storage facilities.
"We are exacting a heavy price from Hamas and the (other) terrorist organizations, and IDF is prepared for a significant expansion of its operations," Israeli Prime Minister Benjamin Netanyahu told reporters Sunday.
The Israeli government also has called up 75,000 reservists and massed tens of thousands of troops and tanks near the border of the border of the Palestinian territory.
The escalation in hostilities has led to an increase in diplomatic efforts in recent days -- with Egypt, France, Turkey, the United States and others wading into the mix after Israel widened its operation and Hamas militants increased its rocket attacks.
The fighting has put new strains on Israel's relationship with Egypt, which is attempting to broker a cease-fire. The Muslim Brotherhood-led government that took power in June has pledged to maintain Egypt's peace treaty with Israel -- the cornerstone of what peace has been achieved in the turbulent region -- but sympathy for the Palestinians runs deep among Egyptians.
The United States and several European countries have put the brunt of the blame for the current crisis on Hamas, saying Israel has a right to self-defense, while Arab and Muslim nations have accused Israel of being the aggressor.
Catherine Ashton, the EU's foreign policy chief, repeated on Monday her previous calls for a long-term solution in Gaza.
"I'm very concerned about the loss of life, but I've also been saying consistently for a long time that we need to find a long-term solution to Gaza," she said. "I've been there three times and we have to find a way to prevent the kind of violent rocket attacks that we've seen, and also to bring some security and peace to the people of that region."
Arab League Secretary-General Nabil el-Araby and 16 foreign ministers from the league's member states will arrive in Gaza on Tuesday for talks, a spokesman for the organization said. Turkish Foreign Minister Ahmet Davutoglu is expected to join the delegation, a ministry spokesman said Monday.
Palestinian Authority President Mahmoud Abbas, meanwhile, will hold talks in the West Bank with the U.N. secretary-general during his visit to the region, said Saeb Erakat, a member of the PLO's executive committee and an Abbas ally.
Hamas, a militant fundamentalist Islamic organization, has political, military, social and religious arms. It took political control of the Palestinian territory in 2007 after a landslide election.
The organization has been branded a terrorist organization by the United States, Israel and the European Union.
CNN's Sara Sidner and Arwa Damon reported from Gaza City; CNN's Chelsea J. Carter reported from Atlanta; CNN's Ben Wedeman, Fred Pleitgen, Amir Ahmed, Jessica Yellin and Mohamed Fadel Fahmy contributed to this report.
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