JERUSALEM -- Israel and Hamas on Monday accepted an Egyptian cease-fire proposal meant to halt a bruising month-long war that has claimed nearly 2,000 lives, raising hopes that the bloodiest round of fighting between the bitter enemies could finally be coming to an end.

Still, both sides signaled a rough road ahead, with an Israeli official expressing skepticism given previous failures, and a Palestinian negotiator saying that "it's going to be tough."

A last-minute burst of violence -- including a deadly Palestinian attack in Jerusalem -- continued bloodshed in Gaza and the reported execution of a number of suspected collaborators with Israel, served as reminders of the lingering risk of renewed violence.

After weeks of behind-the-scenes diplomacy, Israel and Hamas both announced late Monday that they had accepted the proposal for a preliminary 72-hour truce, beginning at 8 a.m. today. Egypt was then set to host indirect talks to work out a long-term truce over the next three days.

"At 8 a.m. local time tomorrow, a cease-fire starts, and Israel will cease all military operations against terrorist targets in the Gaza Strip," Israeli government spokesman Mark Regev said. "Israel will honor the cease-fire and will be watching to see if Hamas does, too."

The war broke out July 8 when Israel launched an air offensive in response to weeks of heavy rocket fire out of Hamas-controlled Gaza. It expanded the operation July 17 by sending in ground forces in what it described as a mission to destroy a network of tunnels used to stage attacks. Israel says the last of the tunnels has nearly been destroyed.

The war has taken nearly 1,900 Palestinian lives, most of them civilians caught in fighting inside Gaza's crowded urban landscape, according to Hamas medical officials. Sixty-four Israeli soldiers have also died, as well as two Israeli civilians and a Thai laborer who worked in Israel. The heavy death toll has eclipsed that of previous rounds of fighting in 2009 and 2012.

A delegation of Palestinian officials from various factions, including Hamas, has been negotiating with Egypt in recent days. Hamas spokesman Fawzi Barhoum said the group had accepted the plan.

"It's clear now that the interest of all parties is to have a cease-fire," said Bassam Salhi, a member of the Palestinian delegation. "It's going to be tough negotiations because Israel has demands too. We don't have any guarantees the siege will be removed."

Hamas is seeking a full Israeli withdrawal from Gaza, an end to an Israeli and Egyptian blockade of the territory, the release of Hamas prisoners held by Israel and international assistance in the reconstruction of Gaza.

Israel says the blockade is needed to prevent Hamas, an Islamic militant group sworn to its destruction, from arming. But the Palestinians and members of the international community have criticized the blockade as collective punishment. The blockade, known to the Palestinians as "the siege," has ground Gaza's economy to a standstill.

Israel has demanded that Gaza become "demilitarized," requiring the unlikely cooperation of Hamas in giving up its significant arsenal.

"We will be putting first on our agenda preventing Hamas from rearming," Regev said. "Ultimately, the Palestinians have a written commitment that Gaza should be demilitarized, and it's time the international community held them to that commitment."

Israel had been signaling in recent days that it was winding down its military campaign. On Sunday, it withdrew most of its ground forces from Gaza, and the army said the pullout was continuing Monday.

In addition, Israel declared a seven-hour pause Monday in its air campaign for what it called a "window" to allow much-needed humanitarian aid into Gaza.

Supermarkets were open for business and more cars were on the streets than during any of the short-lived cease-fires since the war began. Fresh fruits and vegetables were available in outdoor markets.

Despite a drop in military activity, Israel still attacked 38 targets, though well below the levels of recent days.

At least 20 people were killed Monday, including three children -- an 8-year-old girl in the Shati refugee camp and a 12-year-old boy and his 5-year-old sister in the southern border town of Rafah, according to Palestinian medical officials. Still, that was far below the levels during the heaviest fighting.

Israel's chief military spokesman, Brig. Gen. Moti Almoz, disputed Palestinian claims that the vast majority of the dead were civilians.

"We estimate that between 700 and 900 terrorists were killed in direct contact with Israeli soldiers," he told Channel 2 TV. "That's a number that could rise because there were many terrorists inside the tunnels that were probably killed when the tunnels were blown up."

Almoz said Israel expected to destroy the last of the tunnels, allegedly built by militants to stage attacks across the border, in the coming hours.

As the fighting appeared to be tapering off, a Palestinian website close to the Hamas internal security service in Gaza said an unspecified number of Palestinians accused of collaborating with Israel were executed.

It said the alleged collaborators were caught "red-handed" providing information to Israel, including details on certain houses and alerts about planned ambushes. "The resistance will show no mercy to anyone tempted to provide information to the enemy," the al-Majad website said.

In Jerusalem, an assault carried out with a construction vehicle served as another reminder of the tense climate.

Israeli TV stations broadcast a series of amateur videos of the attack, in which a Palestinian man used the front shovel of a construction excavator to ram a bus and tip it over.

Police said a man who worked at the site was run over and killed by the construction vehicle. He was identified as a 29-year-old religious inspector whose job was to ensure that ancient graves were not damaged by construction work.

A policeman who happened to be in the area shot the driver, who was identified as a resident of a Palestinian neighborhood in east Jerusalem. The man's uncle, Hisham Jaabis, said it was a traffic accident and that his nephew had been gunned down in cold blood while trying to dodge the bus. "All of them started shooting at him," he said.

In the past, Palestinian attackers have gone on deadly rampages with bulldozers in Jerusalem traffic.

Shortly after the excavator attack, a gunman on a motorcycle shot and seriously wounded an Israeli soldier in Jerusalem. Police called it a "terrorist" attack, signaling purported Palestinian involvement, and searched for the shooter in east Jerusalem.

Hamas, though it did not claim responsibility for either event, said in a statement: "We praise the heroic and brave operations in Jerusalem, which come as a natural reaction to the crimes and massacres by the Occupation against our people in Gaza."

On Monday, Israeli Prime Minister Benjamin Netanyahu met with the southern command of the Israel Defense Forces, which is leading the war in Gaza, and said that the campaign there was continuing.

"What is about to conclude is the IDF action to deal with the tunnels, but this operation will end only when quiet and security are restored to the citizens of Israel for a lengthy period," Netanyahu said. "We struck a very severe blow at Hamas and the other terrorist organizations. We have no intention of attacking the residents of Gaza."

For Israel, the strategic situation has changed with the takeover in Egypt by the former military general, Abdel-Fattah el-Sissi, who a year ago overthrew President Mohammed Morsi, of the Muslim Brotherhood, which is an ally of Hamas. Morsi did little to prevent smuggling through tunnels, which gave Hamas tax receipts and a mechanism to import cement, weapons and military advisers, Israeli officials insist, from Iran and Hezbollah.

"The big difference this time is that you have an Egyptian leader who understands that Hamas is not just a problem for Israel, but for Egypt, too," one senior Israeli official said. "So the ability of Hamas to bring stuff in is much, much more limited. And because the Gaza tunnels are mostly shut down, the Egyptians have leverage with reopening Rafah. So it is possible to deal far more effectively with illicit transfers, which could make an end game more stable."

Also on Monday, a senior Iranian official said Hamas is able to fire missiles into Israel because Tehran provided weapons technology to the militant group to defend itself against Israeli attacks.

Officials from Iran's Revolutionary Guards have said in the past that Fajr-5 missiles are part of Hamas' Gaza Strip arsenal, whose technology has been supplied by Iran and produced locally without needing direct shipment.

"Palestinian resistance missiles are the blessings of Iran's transfer of technology," the secretary of the Expediency Discernment Council, Mohsen Rezaei, was quoted as saying by Al-Alam, the Arabic channel of Iran's state TV. "We need to transfer defensive and military technology to Palestinians so that they can build weapons under the blockade and defend themselves," he added.

Rezaei, a former Revolutionary Guard chief commander, wrote to President Hassan Rouhani this week calling on him to provide air defense systems to Hamas to hit invading Israeli planes. He also said Hamas should dig tunnels to be used as shelter to protect Gaza's population from Israeli assaults.

"The Americans in recent days approved about $300 million to strengthen [Israel's] Iron Dome. You should provide air defense systems to Palestinians to be able to defend their people against aerial bombardment," he said in the appeal to Rouhani.

Rezaei also urged Hamas to capture Israeli soldiers to use them as bargaining chips in its battle against Israel.

"Getting their soldiers captured is the weak point of Israelis. Should two or three be captured, all Zionists will surrender," he said.

Rezaei said Israel's goal in the ongoing war was to disarm Hamas and destroy its missile power, but that it has failed to do so despite discovering and hitting some underground tunnels.

"The Zionists seized some tunnels but they can't plow the entire Gaza Strip. Facilities where weapons are produced remain intact," he said.

Information for this article was contributed by Josef Federman, Yousur Alhlou, Peter Enav, Mohammed Daraghmeh, Maggie Michael, Ali Akbar Dareini of The Associated Press and by Steven Erlanger of The New York Times.

A Section on 08/05/2014