The Israeli Cabinet will meet early Tuesday to consider a cease-fire proposal that could provide a possible breakthrough in the ongoing crisis.
The proposal, put forward by Egypt, calls for all sides to cease hostilities in Gaza. It also calls for the opening of border crossings, once the security situation is stable, and for high-level talks among those involved.
Senior Israeli officials say the proposal is being taken very seriously; however, a Hamas spokesman described it as a "joke."
"We did not receive this declared paper from the Egyptians ... which means it's an initiative for the media. It's not a political initiative," said Osama Hamdan.
Speaking on CNN's "The Situation Room with Wolf Blitzer," he continued: "It's not really an initiative. It's not really an idea, what they are trying to do is to corner the Palestinians and to help the Israelis more."
Palestinian negotiator Saeb Erakat was more optimistic, saying he is hopeful that "we may see some real, real serious signs of a possible cease-fire in the next 12-24 hours."
"I know that some other leaders in Hamas have said we are not closing any doors for any initiative for a cease-fire," he said.
The stakes are high and climbing.
By Monday, the death toll from nearly a week of Israeli airstrikes on Gaza had reached 186 -- all of them Palestinians -- with at least 1,390 wounded, according to Palestinian health authorities.
The death toll is now greater than the number killed in Gaza during the 2012 war.
"We welcome Egypt's call for a ceasefire and hope this will lead to the restoration of calm as soon as possible," said U.S. State Department spokeswoman Jen Psaki, describing the situation as both dangerous and volatile.
'We have nothing'
Over the weekend, Israel dropped leaflets instructing residents to leave northern areas of Gaza, where it planned to carry out strikes. But Hamas, which controls Gaza, told people to stay put.
Ahmed, a resident of northern Gaza, loaded his family into a taxi Sunday to take them to somewhat safer ground in Gaza City.
"I don't answer to them," Ahmed said of Hamas' request. "I do what's best for us."
As they were getting into the car, explosions erupted nearby, prompting cries of fear from the terrified children.
It's the third time in the last five years that the family has had to flee their home.
Others stayed, because they felt they had no other choice.
"They will not vacate. ... Where do we go?" asked Ramez Al-Madhoun, who lives in a building with 20 people in the northern Gaza neighborhood of Beit Lahya. He said his building is home to seven adults, the rest children.
In Gaza City, where some streets are strewn with rubble, people are taking refuge in U.N. buildings. More than 1,000 gathered in one school alone.
Um Juma'a says she and her family of 15 fled their home at 2 a.m.
"We told the kids, 'Get up! Get up!' " she says. "We walked all the way here."
A baby in the family needs milk, but they don't have any.
"We have nothing," she says. "Not even safety."
No signs of letting up
On Monday morning, the rhythmic thuds of shells fired from Israeli warships pierced the morning silence in Gaza. The streets were relatively quiet with few cars moving around. The buzz of drones filled the skies, a constant reminder of the Israeli aerial presence
Israel has said it will continue the offensive as long as the militant group Hamas keeps firing rockets into its territory.
And Hamas shows no sign of letting up after launching almost 1,000 rockets at Israel.
Caught in the middle are the residents of Gaza. While the Israeli attacks have killed some militants, around 70% of the fatalities were civilians, according to the United Nations. Of the dead, more than 30 are children, the U.N. reported.
"I urgently call on the Israeli Security Forces to put an end to attacks against, or endangering, civilians and civilian infrastructure which are contrary to international humanitarian law," said Pierre Krahenbuhl, commissioner general of the United Nations Relief and Works Agency for Palestine Refugees, or UNWRA.
There are now 17,000 refugees taking shelter in 20 schools in Gaza, UNWRA said, and the airstrikes have damaged 47 of its buildings, including clinics, schools and warehouses.
UNWRA called on Israel to exercise maximum restraint and precaution to avoid more casualties.
"Clearly at this stage not enough is being done in that regard," Krahenbuhl said.
'We cannot live in peace'
Israel said its forces have struck 1,470 "terror targets" across Gaza, including 770 concealed rocket launchers.
On Monday, an Israeli airstrike in Khan Younis, a city in the southern Gaza Strip, struck a motorcycle, killing one member of Islamic Jihad, Palestinian medical and security forces said.
One airstrike hit the house of the head of the Gaza police, Tayseer al-Batsh, killing at least 18 people, all of them members of the same extended family, and wounding 50, Palestinian security and medical sources told CNN on Sunday. The attack, whose youngest victim was 10, happened late Saturday.
Earlier that day, an Israeli airstrike hit a center for the disabled, killing two women.
"Every people in Gaza are suspected as targets to Israel. We cannot live in peace in this situation," said Dr. Ahmed Jarour at Gaza's Shifa hospital, where two patients with severe burns from the disabled center attack were brought in.
On Friday, Israeli rounds struck the El Waffa Hospital.