JERUSALEM — Three weeks into the ceasefire between Israel and Hamas, the number of tents and temporary homes entering Gaza risks falling short of the goals set for the deal’s first phase.

The looming deficit sits at the heart of a dispute between Israel and Hamas that could topple the tenuous truce.

Hamas said it would delay the scheduled release of three hostages on Saturday if Israel did not ramp up delivery of tents, pre-fabricated homes and heavy machinery into the devastated territory, where the majority of people are displaced and many live beside the rubble of blasted-out buildings.

Israel rejects the accusation, and Prime Minister Benjamin Netanyahu has threatened to withdraw from the ceasefire in Gaza and resume the war if Hamas does not release more hostages on schedule.

Getting enough shelter into Gaza has been difficult because aid workers prioritized deliveries of food at the start of the ceasefire. Israeli inspections and restrictions on what can enter Gaza also complicate the process.

The delivery of temporary shelters could soon ramp up, according to officials from Egypt and Hamas who signaled Wednesday that resolution of the dispute was within sight, paving the way for the hostages to be released as planned.

Here’s a look at where things stand with aid into Gaza:

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What Does the Ceasefire Agreement Say About Aid to Gaza?

The ceasefire agreement between Israel and Hamas says that during the first 42-day phase, Israel must allow at least 60,000 temporary homes and 200,000 tents into Gaza. It also must allow entry of an agreed-upon amount of equipment for rubble removal.

Repairs to Gaza’s badly damaged electricity, water, sewage and communications systems — as well as its torn up roads — are to begin during phase one. So is the planning process for rebuilding homes decimated by the war. All of the repairs and planning are being overseen by the U.N. and ceasefire mediators Egypt and Qatar.

Simply removing the rubble — let alone beginning reconstruction — could take decades, according to the U.N. It may also be premature, especially if the ceasefire falls apart and Israel resumes its bombing campaign there. U.S. President Donald J. Trump’s stated intention to rebuild Gaza as the “Riviera of the Middle East” adds uncertainty.

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In the deal’s first phase, Hamas is to release 33 Israeli hostages in exchange for nearly 2,000 Palestinian prisoners. Hamas so far has released 16 of the hostages, in addition to five Thai hostages who were not part of the deal.

Whether the exchanges continue, the agreement says, depends on how the parties adhere to its regulations on humanitarian aid, among other stipulations.

How Many Tents and Temporary Homes Are Getting Into Gaza?

Hamas spokesperson Abdul Latif al-Qanou said Israel had so far permitted 20,000 tents into the territory since the ceasefire took effect on Jan. 19. He said Israel hadn’t let any temporary homes in and was not allowing entry of heavy machinery to remove rubble and recover dead bodies.

COGAT, the Israeli defense body that coordinates the deliveries of humanitarian supplies, disputed part of Hamas’ claims, saying in a statement it had allowed entry of even more tents.

A U.S. official, an Israeli official and aid worker involved in tracking deliveries into Gaza confirmed Hamas’ claim that as of Tuesday morning no prefabricated homes had been allowed in. Both spoke on the condition of anonymity because they were not authorized to talk to the media.

But the aid worker estimated that between 25,000 and 50,000 tents had entered. The Israeli official said at least 30,000 tents had entered.

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Why Has It Been Difficult to Get Shelter Material Inside?

Aid workers say a number of factors are complicating the quick delivery of tents and other temporary shelters into Gaza. For one, the priority at the start of the ceasefire period was getting food and water into a territory on the brink of famine.

Shaina Low, communications adviser for the Norwegian Refugee Council, said humanitarian groups “prioritized bringing in food during the first couple of weeks of the ceasefire to address Gaza’s acute starvation crisis.”

Also, anticipating “mass population movements,” aid groups held back from sending tents in immediately because people would have a hard time carrying them along with all their belongings, she said.

The latest report from the coalition of groups tracking population movement in Gaza says that at least 586,000 Palestinians have gone north since late January and over 56,000 have moved south.

Ramping up shelter supplies so suddenly proved a tall order, said Tania Hary, the director of Gisha, an Israeli organization dedicated to protecting Palestinians’ right to freedom of movement. She added that the initial focus in the first days of the ceasefire was meeting the threshold of 600 trucks a day.

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“They’re scrambling to get in all the tents in their pipeline,” she said. “Getting in 60,000 caravans is a huge production.”

There is another factor slowing the pace of aid deliveries: Israel deems some items “dual-use,” meaning they could potentially be diverted for military means.

According to a list circulated to humanitarian aid groups by COGAT, “mobile homes” and large tents require Israeli inspection, even though they are on the list for being fast-tracked. The same goes for cleaning materials, water trucks, generators, metal waste containers, sewer inspection devices and iron waste containers.

Large storage tents, desalination facilities, toilets and showers with certain kinds of metal, x-ray machines and diesel generators require an even more intense approval process.

What Does This Mean for the Deal?

Mediators were hopeful Wednesday they could resolve the dispute by Saturday and get the ceasefire back on track.

An Egyptian official with knowledge of the talks said the two sides were close to an agreement. The official, speaking on condition of anonymity to discuss private negotiations, said Israel had committed to delivering more tents, shelters and heavy equipment to Gaza.

An official with Hamas, Mahmoud Merdawi, cited “positive signals” that the hostages would be released on Saturday. But he cautioned that the group had yet to receive the guarantees it seeks from Israel regarding the delivery of humanitarian aid.