Gaza City (CNN) -- Will it, or won't it, hold?
That's the question following word late Monday that Israel and Palestinian factions, including Hamas, agreed to a 72-hour humanitarian cease-fire proposed by Egypt.
Even as they agreed to the cease-fire, set to take effect Tuesday morning, both sides appeared suspicious of one another.
"The onus is on Hamas," Israeli government spokesman Mark Regev said shortly after announcing on CNN's "The Lead with Jake Tapper" that Israel had accepted the Egyptian proposal. Under the agreement, the cease-fire will begin at 8 a.m. local time, he said.
"We are entering this with our eyes open. ...We have been burnt more than once."
The sentiment was similar from Hamas spokesman Osama Hamdan, who told CNN as long as Israel honors the agreement, so will the Palestinians.
"We hope they can take it and be committed to a cease-fire," he said.
While Egypt has not released details of the cease-fire agreement, Regev said it was the same agreement that Israel accepted and Hamas rejected three weeks ago.
News of the cease-fire comes as Israeli Prime Minister Benjamin Netanyahu vowed Monday to finish the military operation to destroy Hamas' network of tunnels.
That operation appeared to be close to an end, with Regev saying Israel will "cease all our ... military activities, all our offensive operations against terrorist targets in the Gaza Strip."
When asked about the tunnels, he said the issue is solving itself. "It's winding up anyway," Regev said.
Earlier in the day, the Israel Defense Forces said there were possibly between one and three tunnels left.
Mounting death toll
Both sides have been under fire for a mounting death toll in the conflict, now in its fourth week.
More than 1,800 people have been killed in Gaza, according to the Palestinian Health Ministry. The United Nations has said of those casualties, civilians account for 70% to 80%.
Israeli officials have said 64 Israeli soldiers and three civilians in Israel have died.
The United States urged both sides to honor the cease-fire agreement.
"The United States has been steadfast in our insistence on an end to rocket and tunnel attacks against Israel and an end to the suffering of the people of Gaza," State Department spokeswoman Jen Psaki said.
On Monday, during a short humanitarian "pause" in the fighting called by Israel, residents in Gaza flooded the streets to pick up supplies and check on their abandoned homes.
Al Saha, the largest open-air market in Gaza City, was bustling with vendors. One man hung clothes for sale from the burned-out carcass of a bus hit a few days ago by Israeli fire power.
Cars jammed Gaza's main thoroughfare, but the atmosphere appeared relaxed, and children played in the street.
The Palestinian Health Ministry said at least 18 people were killed in Gaza during the cease-fire, including an 8-year-old in a strike on a house in a refugee camp in Gaza City.
That strike also injured 30 people, Palestinian health officials said, and happened after Israel had started the cease-fire.
Israel said that strike did not violate the cease-fire because it happened just two minutes into it and the operation had already been in progress.
Hamas had not agreed to the Israeli-declared cease-fire, and at least 53 rockets were fired from Gaza into Israel on Monday, according to the IDF.
Daniel Mansour, a senior Palestinian Islamic Jihad operative in charge of intelligence-gathering in northern Gaza, was targeted and killed before the cease-fire Monday, the IDF said. He had participated in directing rocket attacks toward Israel, the IDF said.
Two attacks in Jerusalem
Police in Jerusalem said they foiled what they described as a terror attack when they shot and killed the driver of an earthmover after it overturned a passenger bus.
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.
The driver of the earthmover was identified as 20-year-old Mohammed Jaabis, a Palestinian from the East Jerusalem neighborhood of Jabal alMukaber.
Footage broadcast by Israel's Channel 10 showed the earthmover still moving as security forces approached. The video appeared to show shots being fired.
The incident happened in the Sheikh Jarrah area of central Jerusalem, near the entrance to a Jewish orthodox neighborhood.
Hamas praised the attack and said it was "a natural reaction to the Israeli crimes against civilians" in Gaza.
In another incident, a man on a motorbike opened fire at an Israeli soldier near Hebrew University, Israeli police spokesman Micky Rosenfeld said. Rescue workers said the Israeli was severely wounded.
An eyewitness on Israel Channel 10 said he heard a gunshot and saw "a soldier holding his chest. He walked a few steps backwards and collapsed."
International condemnation of Israel and Hamas
France is the latest country to condemn the Gaza operation and strikes on U.N.-run shelters in Gaza.
"How many deaths will it take to stop what has to be called the carnage in Gaza?" French Foreign Minister Laurent Fabius asked in a statement. He said while Israel has a right to total security, "this right does not justify the killing of children and the slaughter of civilians." He also said Hamas carries an overwhelming responsibility in this "macabre gearing which particularly serves extremism."
On Sunday, the United States and the United Nations used the strongest language yet in condemning the strike on a U.N.-run shelter in Gaza, with Washington calling the attack "disgraceful."
At least nine people at the school, which was being used as a shelter for about 3,000 people, were killed in the shelling.
Israel said it is carefully reviewing the attack.
The IDF said it targeted three Palestinian Islamic Jihad members riding a motorcycle in the vicinity of the school, but didn't say if the suspected militants were hit.
CNN's Wolf Blitzer, Tal Heinrich, Saima Mohsin and Ali Younes contributed to this story