A three-day cease-fire that ended the round-the-clock carnage and terror in Gaza and southern Israel was holding Wednesday ahead of negotiations in Cairo on a longer-term truce and perhaps a broader deal for the ravaged Gaza Strip.

Over the coming days, Egyptian mediators plan to shuttle between Palestinian and Israeli delegations to try to work out an agreement.

U.S. Secretary of State John F. Kerry, speaking in an interview with the British Broadcasting Corp., urged both sides to take advantage of the Gaza truce to move toward broader negotiations.

Asked whether he supported Palestinian demands for a lifting of Israel’s blockade of Gaza, Kerry said: “What we want to do is support the Palestinians in their desire to improve their lives and to get food in and to open crossings and to reconstruct and have greater freedom.”

But that must come “with a greater responsibility toward Israel, which means giving up rockets,” he said, referring to the barrages unleashed by Hamas and other Palestinian militant groups in the Gaza Strip. “No country can live with that condition, and the United States stands squarely behind Israel’s right to defend itself in those circumstances. Period.”

Kerry said all this would come together only with a “bigger, broader approach to the underlying solution of two states” that would provide security for Israel and “a better life and greater freedoms for the Palestinians.”

After nearly a month of grinding war, Gaza and southern Israel were experiencing something new: calm. Since the Egyptian-brokered cease-fire kicked in Tuesday morning at 8 a.m., there have been no rocket attacks or missile strikes. No tunnel infiltrations or shelled schools.

But there have not been any celebrations or declarations of victory, either. Just a single, haunting question: If this war is truly over, how long until the next one begins?

Cars and donkey carts loaded with household goods and mattresses filled the streets of Gaza on Wednesday and people lined up at banks to withdraw money, witnesses said. Hundreds of people went to inspect their flattened homes.

Both Israel and Hamas went into the fight seeking to change the underlying dynamics of a situation that has produced three rounds of combat in less than six years while crippling the Gazan economy. But after 29 days of fighting that claimed nearly 2,000 lives, it is far from clear that either side has succeeded.

That could mean the next round of battle kicks off in the coming few years, months or even days if both sides do not get enough of what they want during the negotiations beginning Wednesday in Cairo.

Hamas leaders have repeatedly said they seek an opening of Gaza’s border crossings, the release of Palestinian prisoners and international assistance in rebuilding the territory’s shattered economy, among other demands. Israel wants a demilitarization of the strip and a promise of an end to the rocket fire.

Israel on Tuesday withdrew its remaining ground forces from Gaza just ahead of the 72-hour truce’s start time as both sides fired their final barrages.

An Israel Defense Forces spokesman, Lt. Col. Peter Lerner, said Israel “would continue to maintain defensive positions from the air, from the coast and from the ground” just outside Gaza and that all would be prepared to return fire if the rocket strikes resume.

By Israel’s own admission, Hamas still has at least several thousand rockets despite firing 3,300 and losing an additional 3,000 to Israeli attacks. Hamas has reserved the right to dip deeper into its arsenal if Israel fails to yield to the group’s demands.

“They are still intact,” Mkhaimer Abusaada, a political-science professor at al-Azhar University in Gaza, said of Hamas. “They are not broken. They did not wave a white flag. It’s still a very strong resistance organization.”

In some ways, Abusaada said, the group is even stronger than it was at the war’s start, despite enduring weeks of Israeli bombardment.

Hamas has used its decades-long fight with Israel to rally support, and when the war began, the group was badly in need of it. Diplomatically isolated from Arab powers and facing a financial crunch from the closure of its smuggling tunnels, the group could not even afford to pay its 44,000 government employees.

But the four-week war, in which Hamas launched rockets deeper into Israeli territory than ever before and used tunnels to carry out deadly infiltrations, has boosted the group’s image among many Palestinians.

It has also brought the group’s leaders to the negotiating table, where they will be able to make their demands and possibly win economic concessions that are now needed even more desperately.

“Now, Hamas is no longer isolated,” Abusaada said. “The Americans are negotiating with them indirectly. The Israelis are negotiating with them indirectly.”

But the Israelis are deeply reluctant to give Hamas anything that could be perceived as a reward for its militancy, and they hope that Gaza residents will ultimately blame Hamas for a war that has left approximately 1,800 Palestinians dead with little to show for it.

An Israeli military official said Tuesday that Hamas had been badly depleted by some 4,800 Israeli strikes on Gaza over the past month. The attacks destroyed hundreds of Hamas command centers and weapons facilities and killed about 900 militants, Israel’s military says. Troops also dismantled 32 tunnels, 14 of which connected directly to Israel.

By contrast, the official said, Hamas failed to land its punches.

“They can tell a narrative that they did damage to Israel, but really the damage is quite limited,” said the official, who was not authorized to speak on the record.

Still, there was little sense of triumph in Israel on Tuesday, and not only because many are still mourning 64 dead Israeli soldiers and three civilians.

On Israel’s political left and right, there were apprehensions that Israeli Prime Minister Benjamin Netanyahu will not use the conflict to try to create a new order in Gaza that does not involve recurring bouts of war.

The cease-fire was greeted with scorn by hard-line members of Israel’s cabinet who want the government to topple Hamas and put Gaza under an international mandate.

“This situation of limbo — no war, no peace — is the worst scenario for Israel,” Israeli Foreign Minister Avigdor Lieberman said in an interview. “We can’t survive having another conflict every two or three years.”

On the other side of Israel’s political spectrum, Labor Party leader Isaac Herzog said he, too, fears that the apparent end of this conflict could merely set the stage for the next.

But he said Israel now has an opportunity to use the Cairo talks to empower the relatively moderate government of Palestinian Authority President Mahmoud Abbas and restore him to Gaza, seven years after his forces were routed from the territory by Hamas.

Abbas’s government will lead the Palestinian delegation in Cairo, which will also include representatives of Hamas and the Islamic Jihad group.

“There’s a clear convergence of interests between Egypt, Jordan, the Gulf states, Israel and the Palestinian Authority in recognizing that we need to combat terrorism and move toward peace,” Herzog said.

That’s also a U.S. goal, and Washington has sought ways to shore up Abbas’s credibility as the leader of all Palestinians.

Economic or practical improvements for Gazans are one likely way to do that if Israel agrees and Hamas cedes greater control to its longtime rival. The United States would be expected to be a major donor and facilitator, but large questions remain about how economic development can coexist with security measures to partly demilitarize Gaza and prevent Hamas from re-arming.

Israeli officials expressed skepticism Tuesday that the talks could succeed in delivering much more than a fragile and temporary truce. Hamas remains the de facto power in Gaza, they said, and the group has no interest in changing that.

“A whole different relationship could be built, but the chances of that happening are not all that great,” said an Israeli official who spoke on the condition of anonymity because he was not authorized to speak on the record.

The official said the one major difference between these talks and the Cairo-based negotiations that ended the last war between Israel and Hamas is that Egypt has a new government that is much more hostile to the Palestinian group.

While Hamas was able to use tunnels beneath the Egyptian border to smuggle in weapons after the 2012 fight ended, that will be more difficult now that Egypt’s military-backed government has effectively shut the tunnels down.

“That may be the game-changer,” the official said. “If there is one.”

Raghavan reported from Gaza City. Deane reported from Rome. Orly Halpern in Jerusalem and Islam Abdel Karim in Gaza City contributed to this report.