(CNN) -- A temporary humanitarian cease-fire declared by Israel began Monday in Gaza without the agreement of Hamas.
It expired seven hours later amid claims and counterclaims of attacks.
Israel's Prime Minister Benjamin Netanyahu said his country is close to concluding its action to destroy Hamas tunnels but that the military operation will end "only when quiet and security are restored to the citizens of Israel for a lengthy period."
As the death toll continues to rise and any deal to halt hostilities between the two bitterly opposed sides appears far off, here's an explanation of key elements of the nearly four-week conflict.
What's the latest?
The seven-hour humanitarian cease-fire declared by Israel began at 10 a.m. local time (3 a.m. ET) Monday, but a senior Hamas spokesman said the group had not agreed to it.
The Israeli military had said the truce would not apply to the areas in which Israeli soldiers were currently operating, such as Rafah, and warned that it would "respond to any attempt to exploit this window to harm Israeli civilians and IDF soldiers."
The Gaza Health Ministry said Israeli forces carried out a strike on a house in a refugee camp in Gaza City 20 minutes after the cease-fire took effect. The strike killed an 8-year-old girl and wounded around 30 people, most of them children, a spokesman said.
Israel denied the claim, saying all offensive operations had ceased as it had declared they would. A spokesman later confirmed that a strike had taken place at 10:02 a.m. but said that it did not breach the cease-fire as it was an ongoing operation targeting "terrorists from Islamic Jihad."
The Israel Defense Forces said three rockets had been fired into Israel from Gaza since it began the cease-fire.
Meantime, police in Jerusalem said they foiled what they described as a terror attack when they shot and killed the driver of an earthmover, who had overturned a passenger bus in the central Sheikh Jarrah area of the city. Police said one pedestrian was also killed and the bus driver was injured. There were no passengers on the bus at the time, police said.
In another incident, a man on a motorbike opened fire at an Israeli soldier near Hebrew University, police said. Rescue workers said the Israeli was severely wounded.
Why didn't Hamas sign on to Monday's cease-fire?
In an exclusive interview with CNN's Nic Robertson on Sunday, Hamas' Qatar-based political leader Khaled Meshaal said Israel's condition that it be able to continue destroying militant tunnels meant that it was not truly a cease-fire.
"The presence of the Israeli forces inside Gaza and destroying the tunnels means it's an aggression, because they are inside the Gaza territories," Meshaal said, according to a CNN translation.
Meshaal said he would only support a long-term cease-fire if Israel changed its policy restricting the movement of goods and people into Gaza.
"There are two kinds of cease-fires: There is the humanitarian cease-fire, like 72-hour cease-fire that was meant to help and aid our people getting food, water, and help collecting the bodies. As far as the sustainable cease-fire, this is connected to an agreement accepted by the two parties that will guarantee our Palestinian demands headed by lifting the siege on Gaza," Meshaal said.
The political leader said he was still willing to engage in talks with Egyptians acting as the go-betweens.
Didn't the U.S. describe an Israeli attack this weekend as 'disgraceful'?
Israel's tactics are coming under increasing international criticism after a series of deadly strikes on or near U.N. shelters housing displaced civilians in Gaza.
After the latest incident, in which at least nine people were killed Sunday, the U.S. government said Israel must "do more to meet its own standards."
"The United States is appalled by today's disgraceful shelling outside an UNRWA school in Rafah sheltering some 3,000 displaced persons, in which at least 10 more Palestinian civilians were tragically killed. The coordinates of the school, like all U.N. facilities in Gaza, have been repeatedly communicated to the Israeli Defense Forces," the State Department said.
"The suspicion that militants are operating nearby does not justify strikes that put at risk the lives of so many innocent civilians," it said.
The IDF said that it targeted three Palestinian Islamic Jihad members riding a motorcycle in the vicinity of the U.N. building and that it was reviewing the consequences of the strike.
But U.N. Secretary-General Ban Ki-moon said the attack was "yet another gross violation of international humanitarian law."
The Israeli military says it doesn't intentionally target U.N. facilities.
Who is fighting?
Israel, the biggest recipient of U.S. foreign aid, is battling Hamas, the Palestinian militant organization that controls Gaza. Other armed groups in Gaza, a coastal territory about the size of Detroit, are also fighting alongside Hamas.
The Israeli military launched Operation Protective Edge against Hamas in Gaza on July 8, saying it wanted to put a stop to rockets being fired over the border. The conflict began with waves of Israeli airstrikes on Gaza amid barrages of Hamas rockets fired into Israel. But on July 17, Hamas fighters used a tunnel under the border to attempt an attack on Israeli soil. Israel responded by sending thousands of ground troops into Gaza with the stated aim of destroying the network of underground tunnels.
What does each side want?
Hamas says it wants Israel to lift a blockade it began on Gaza in 2007, a measure Israel has said is necessary to stop Hamas and other allied militant groups from bringing weapons into the territory. Israel has been criticized for tightly restricting the movement of goods and people, with aid groups accusing it of cutting off basic supplies and creating a humanitarian crisis.
Hamas also wants the release of large numbers of Palestinians who were detained in June after the kidnapping of three Israeli teenagers in the West Bank. The teenagers were later found dead in a field, heightening the tensions that led to the Gaza conflict.
Israel wants to halt the rocket fire from Gaza and demolish the labyrinth of tunnels underneath the territory. More broadly, it says it wants the demilitarization of Gaza to permanently remove the threat posed by Hamas to its citizens.
Netanyahu last week described the current operation as the first phase of demilitarizing Gaza.
In comments at an IDF conference Monday, Netanyahu said the operation would continue beyond the tunnel actions and called on the international community to demand "that the rehabilitation of Gaza be linked to its demilitarization."
What has been the human cost of the conflict?
The heaviest casualties have come where the fighting has been concentrated: in crowded areas of Gaza.
More than 1,800 Palestinians have been killed in the densely populated territory since July 8, the Gaza Ministry of Health says, and more than 9,000 have been wounded.
At least 69% of the dead are civilians, according to the U.N. Office for the Coordination of Humanitarian Affairs, including more than 350 children and nearly 200 women.
Many of the injuries that doctors have had to treat are severe.
Mohammed Salam, an emergency room doctor in one Gaza hospital, reeled off a list of what he was seeing: "Shrapnel and fractures and explosives injuries; open wounds; cut, amputated lower limbs -- mainly amputated lower limbs."
On the Israeli side, 64 soldiers and three civilians have been killed. Israel's Iron Dome missile defense system has helped significantly reduce civilian casualties in the country, intercepting many of the more than 3,000 rockets fired from Gaza.
The indiscriminately fired rockets have varying ranges, putting most of Israel under threat. Residents have to scramble for bomb shelters when the warning sirens go off.
But many people in Gaza have little in the way of shelter. The United Nations estimates that as many as 485,000 Gaza residents may have been displaced by the fighting, roughly a quarter of the territory's population.
Hospitals and morgues have been overwhelmed. The electricity supply has been out since early last week. And most people have extremely limited or no access to water, deepening the humanitarian crisis.
Who's responsible for the high number of civilian deaths?
As with much in this conflict, each side blames the other.
Israel says Hamas fighters hide behind civilians and put weapons and military infrastructure in populated areas, like homes, mosques, hospitals and schools.
The Israeli military argues that although it strives to minimize civilian casualties, Hamas' approach draws the fighting into densely populated areas.
But human rights activists have slammed Israeli forces for using imprecise weapons like artillery in crowded residential areas. And U.S. officials have stepped up calls for Israel to do more to avoid civilian casualties.
Are there any talks at the moment?
Efforts to find a way out of the violence have continued in Cairo, Egypt, but so far without Israel.
Egyptian President Abdel Fattah el-Sisi touted a cease-fire initiative as a "real chance" to stop the bloodshed and the best way to get help into Gaza and launch talks.
An Egyptian proposal put forward last month was accepted by Israel but rejected by Hamas, which said the plan didn't address its broader concerns.
Members of a Palestinian delegation arrived in Cairo on Saturday to attend the negotiations, the Egyptian state-run news agency MENA reported.
The delegation included a representative of Fatah and Palestinian intelligence, with Hamas and Islamic Jihad representatives set to arrive later, the report said.
But Israel said it wasn't sending a delegation to Cairo.
The Egyptian government helped broker the cease-fire between Israel and Hamas in the 2012 conflict in Gaza. But that was under former President Mohamed Morsy, who was ousted by the military last year.
The current president has much worse ties with Hamas than Morsy, who was backed by the Islamist Muslim Brotherhood.
This time around, the United States, the United Nations and Egypt are all trying to engineer a peace deal, but so far without success.
"There is not a single mediator among them that's trusted by both sides," Aaron David Miller, a former Middle East negotiator for the U.S. government, wrote in an opinion article for CNN.
How has the United States responded to the conflict?
The United States, Israel's staunchest ally, has throughout the conflict repeated its support for Israel's right to defend itself. Secretary of State John Kerry, meanwhile, has worked hard to try to broker a cease-fire, but with little success.
As the death toll continues to mount and anger grows over the strikes on U.N. shelters, U.S. officials have increased calls for Israel to improve its efforts to avoid civilian casualties.
Those concerns didn't stop the United States from agreeing to Israel's request to resupply it with several types of ammunition, a U.S. defense official told CNN last week.
Publicly, U.S. and Israeli officials have tried to display solidarity.
Over the weekend, Netanyahu praised what he called U.S. President Barack Obama's "unequivocal stand with Israel on our right to defend ourselves" as well as the "untiring efforts" of Kerry.
But tensions have been reported behind the scenes.
Netanyahu didn't deny a report that he told Kerry and U.S. Ambassador to Israel Dan Shapiro "not to ever second guess me again" on how to deal with Hamas, though he said the report did not reflect the general "tone and substance" of calls between them.
How are the Arab nations reacting?
Analysts say this conflict is unusual because many Arab states are supportive of Israel's offensive against Hamas.
Countries like Egypt and Saudi Arabia are viewed by experts as being more concerned by Islamic fundamentalist movements than they are about Israel.
Hamas is an offshoot of the Muslim Brotherhood movement, which is the target of a crackdown by Egypt and feared by some other Arab governments in the aftermath of the Arab Spring.
In the new order in the Middle East, support for Hamas is believed to come more from Iran, Qatar and Turkey.
What is the mood in Israel?
The Israeli public has shown strong support for the military operation in Gaza.
According to a poll conducted by the Sarid Institute for the Israeli broadcaster Channel 10, 63% of Israelis are against ending the operation at this moment. That was nonetheless down from 81% last week.
The survey, whose results were made public Sunday, found that 56% of Israelis believe Netanyahu is doing a good job, a slight increase over last week.
CNN's John Vause, Tal Heinrich, Jake Tapper and Dana Ford contributed to this report.