In April, Israel suspended the delivery of cement to Gaza for private individuals intending to reconstruct homes destroyed in the 2014 war, accusing an official in Gaza’s economy ministry of siphoning construction materials for other purposes. The ministry denied the allegations.

About 4,065 of the 17,800 destroyed homes, or 23 percent, have been reconstructed, according to data from the United Nations, which is overseeing the mechanism for importing construction materials. An additional 5,095 homes were in the process of being rebuilt but the work has been halted because of the Israeli suspension.

Among those are the home of a woman from Beit Hanoun, who is 42 and said that when she received her first voucher to buy cement from an approved vendor, he had nothing to sell her. At the same time, the woman — who, like a dozen border residents interviewed spoke on the condition of anonymity so they could speak frankly about Hamas and to avoid tipping off the Israeli military — and her relatives have been jolted awake over the past year by trucks rolling by at night, she said.

Residents said they had heard thudding noises below an incongruous-looking nearby shack that they think covers a tunnel entrance. They said they were too afraid to ask the truck drivers or other men they see around the shack what was going on.

“How can we say they are helping when they are building tunnels?” a woman asked of Hamas, tapping the rubble under her feet.

Naji Sarhan, the deputy housing minister in Gaza, denied that Hamas was taking construction material, particularly cement, intended for reconstruction, instead accusing vendors of illegally selling their supplies on the black market. He said Hamas had “its own ways” to obtain building materials.