Both sides halted cross-border attacks as the three-day truce took effect at 8 a.m. (0500 GMT). The shelling stopped and in Gaza City, where streets had been deserted during the war, traffic picked up and shops started opening.
If the calm holds, it would be the longest lull in almost a month of fighting that has killed nearly 1,900 Palestinians and 67 Israelis.
In coming days, Egyptian mediators plan to shuttle between Israeli and Palestinian delegations in Cairo to try to work out new arrangements for Gaza.
As details of the Palestinian demands emerged, there were some signs that Hamas is willing to give Palestinian President Mahmoud Abbas a role in Gaza as part of rebuilding efforts.
Hamas seized control of Gaza from Abbas' Palestinian Authority in 2007, prompting the Egyptian-Israeli blockade of the territory. Abbas' return would presumably aim to reassure Israel and Egypt, allowing an easing of the closure.
The Palestinian delegation in Cairo presented a joint list of demands to Egypt, said Hana Amireh, a West Bank-based PLO official who is in touch with the delegation.
The demands include a call for internationally funded reconstruction that would be overseen by an Abbas-led government that was formed in a unity deal with Hamas right before the war.
The delegation is led by one of Abbas' confidants but includes members of Hamas and other factions.
Efforts are under way to arrange a pledging conference of donor countries in Norway at the beginning of September, Mohammed Mustafa, the West Bank-based deputy prime minister of the technocrat government, told The Associated Press.
However, Hamas official Izzat Rishq suggested that while the group will seek a role in the actual reconstruction.
"We know that we have a national unity government that can handle the donors' conference and the rebuilding, but implementing it on the ground requires national cooperation," he said.
A three-member Israeli delegation arrived in Cairo on Tuesday evening, according to an airport official who spoke on condition of anonymity because he was not authorized to speak to the media.
The situation on the ground remains volatile, and any cease-fire violation could quickly derail the Cairo talks. Gaps between the Israeli and Palestinian positions are wide, and it's not clear how much can be achieved.
Yossi Kuperwasser, a senior official in Israel's Ministry of Strategic Affairs, said Israel is willing to discuss an easing of Gaza border restrictions, but needs guarantees that Hamas will not be able to re-arm.
He said the international community "can have a role in securing the security arrangements that are going to be agreed upon in Gaza," including preventing the entry of goods that could be diverted by Hamas for military purposes.
Israel is concerned that Hamas would be able to restock its military arsenal if the borders are opened.
Over the years, Hamas has smuggled rockets and other weapons into Gaza through smuggling tunnels under the Gaza-Egypt border. The flow only halted after a new government in Egypt took over a year ago and destroyed the tunnels.
Israeli Prime Minister Benjamin Netanyahu has repeatedly raised the idea in recent days of disarming Hamas, with the help of the international community.
Hamas is deeply rooted in Gaza and still has thousands of armed men under its command.
As Tuesday's truce took effect, residents returned to devastated areas to inspect the damage.
One of the hardest-hit areas of recent days was the southern Gaza town of Rafah, which had come several days of heavy Israeli shelling and airstrikes, starting Friday, after Israel suspected one of its soldiers had been captured by Hamas. Israel later said the soldier was killed in battle.
"I never saw anything like this in my life," Tawfiq Barbakh, a 67-year-old father of 12, said as he surveyed his badly damaged home. "I don't know how many shells landed every minute but it felt like 20 or 30."
The current round of confrontations began with the June 12 abduction-killing of three Israeli teens in the West Bank, blamed by Israel on Hamas, followed by the apparent revenge killing of a Palestinian-American teen, the roundup of hundreds of Hamas activists by Israel, and finally barrages of Gaza rocket fire on Israel.
Israel launched airstrikes on July 8 it said were aimed at stopping the rocket fire before expanding the operation on July 17 by sending in ground forces to destroy a network of tunnels used to stage attacks.
The fighting has claimed nearly 1,900 Palestinian lives. The war has also left 67 dead on the Israeli side, all but three soldiers.
The U.N. and Gaza human rights groups monitoring the death toll have said more than 75 percent of those killed in Gaza were civilians.
But an Israeli military spokesman, Lt. Col. Peter Lerner, said Tuesday that about 900 Palestinian militants had been killed by Israeli forces during the war.
Another military official had earlier told the AP that at least 300 militants were killed. Asked about the sharp jump in figures over just two days, Lerner said the figure of 900 militants killed was an approximation, based on reporting from individual Israeli units.
Lerner said troops destroyed 32 cross-border tunnels built for attacks inside Israel.
He said that over the past month, Hamas and other Gaza militants had fired some 3,300 rockets and mortar rounds at Israel and estimated that Israeli forces had destroyed another 3,000 rockets on the ground — but that Hamas has an equal number left for future use.
Palestinian police, meanwhile, said that one of the rockets fired from Gaza before Tuesday's cease-fire hit a home in the town of Bethlehem in the West Bank, causing damage, but no injuries.
Enav reported from Jerusalem. Associated Press writers Ibrahim Barzak in Gaza City, Hamza Hendawi in Rafah and Maggie Michael in Cairo contributed to this report.
Copyright 2014 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.