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.
The Israeli military said it was investigating the strikes but said that Hamas often hides missiles and other weapons in hospitals and private homes.
Iron Dome intercepting attacks
Israel has used its Iron Dome defense system against some of the more than 980 rockets fired from Gaza into Israel, the military said.
On Monday, the system intercepted a rocket fired from Gaza toward the Israeli border town of Sderot, close to CNN's Blitzer.
"We heard a loud boom," he said. "If you don't seek shelter, you're gonna be in danger because even though the rocket was destroyed in the air, the shrapnel starts coming down very, very quickly."
When sirens go off, people along the border have about 15 second to seek shelter. Farther north in Tel Aviv, where the Iron Dome system also intercepted a rocket Monday, people have about a minute.
On Sunday, militants launched more than 130 rockets at Israel. The defense system intercepted 22 of them.
Seventy percent of Israel's population lies within range of Hamas rocket attacks, according to the Israel Defense Forces, and the Iron Dome can't stop all of them.
One rocket that hit the city of Ashkelon on Sunday severely wounded an Israeli teen, the IDF said.
So far, no Israelis have been killed by the rocket attacks.
The IDF said Monday that it shot down a drone spotted along the Israeli coastline, near the city of Ashdod.
Hamas' military wing said in a brief statement that it has sent a number of drones on missions inside Israel and would provide more details in due course.
Al Aqsa TV in Gaza showed video of a drone it called Ababill 1, a name inspired by the Quran meaning "consecutive waves."
Hopes of a cease-fire
So far, international efforts to press Israel and Hamas into negotiating a cease-fire have failed to gain traction.
Secretary of State John Kerry was preparing a possible trip to the Middle East to lay groundwork for a cease-fire, but several U.S. officials told CNN Monday night that Kerry is postponing the visit to give Egyptian efforts a chance to take root.
Kerry was to travel from Vienna -- where he was negotiating a deal with Iran and world powers over Iran's nuclear program -- to Egypt and Qatar in the coming days to lay the groundwork for a possible cease-fire between the two sides.
One official said the United States wants to give Egypt a chance to reassert itself as a power broker the Middle East, as it did during the 2012 cease-fire. The United States sees the election of President Abdel Fattah al-Sisi as a positive development in terms of Egypt playing a constructive role in the conflict, because Obama administration sources say that North African nation now is viewed as less conciliatory towards Hamas than it was under former President Mohammed Morsy.
Kerry will allow a few days for diplomatic efforts to lay any groundwork, officials said, and is still prepared to either travel to the region if any cease-fire does not take hold, or to help support it if it does.
"Diplomacy has to start with Hamas," a senior U.S. official said. "They are the ones firing the rockets, and from (Israeli Prime Minister Benjamin Netanyahu's) point of view, he is just responding."
Earlier, Kerry spoke by phone with Netanyahu and expressed U.S. concerns about escalating tensions. He reiterated that the U.S. is prepared to help bring about a cease-fire, a senior State Department official said.
But "offering facilitation is not enough," Yousef Munayyer of the Washington-based Palestine Center told CNN's "New Day."
"It's important that the United States demand a cease-fire," he said. "There is no military solution to this."
On Monday, Ismail Haniyeh -- former prime minister and Gaza-based deputy chief of Hamas -- said that talks must take into account the situation on the ground.
"All diplomatic efforts must consider our demands. We cannot let the blood of our martyrs and the suffering and sacrifices of our people go to waste," he said.
"There are talks between several countries and with our political leadership abroad, but all must consider the reality on the ground. The resistance is steadfast against this aggression and cannot be written off."
The last cease-fire with Gaza was negotiated in 2012 and included Egypt and the country's now ousted President, Morsy.
His Muslim Brotherhood was closer to Hamas than Egypt's current government, which has been reluctant to open border crossings for Palestinians.
Tensions in the West Bank
The Gaza conflict flared after the kidnapping and killing of three Israeli teenagers in the West Bank set off a new cycle of violence in the region. The Jewish teens' bodies were found in a field two weeks ago.
Two days later, a Palestinian teenager -- Mohammad Abu Khedair -- was abducted and killed in Jerusalem, raising tensions further.
Seven suspects were arrested, according to Israel's domestic security service. They did not previously know their victim and two of the suspects first attempted to attack and kidnap an 8-year-old boy, the service said. The attempt was foiled by the boy's mother.
The kidnappers then patrolled Jerusalem Arab neighborhoods trying to locate a victim, until finding the teenager, the service said.
Since the Israeli youths went missing last month, Israeli security forces have been hunting for their abductors in the West Bank. Israel blames Hamas for the Jewish teenagers' deaths, an accusation the group denies.
The weeks-long Israeli search in the West Bank has stirred anger among residents, resulted in hundreds of arrests and provoked deadly unrest.
Early Monday, a 21-year-old Palestinian named Munir Ahmad Badareen was shot and killed during clashes with the Israeli military south of Hebron, said Rateb Jabour, a member of a local committee.
Badareen was left bleeding on the ground for 40 minutes before the Israeli military allowed a Palestinian ambulance to transfer him to a hospital, Jabour said.
A spokeswoman for the Israeli military said the matter would be investigated by the military police, whose findings would be reviewed by the military advocate general.
The death came as Israeli security forces detained 57 people in the West Bank late Sunday into early Monday, the Palestinian Prisoner's Society said. The detentions bring the total number of people arrested since the Israeli operation began last month to 1,071, including 34 Palestinian members of parliament, the organization said.