This was a military hospital from 1948, when Israel fought its war of independence, until 1953. It has since operated as a civilian hospital that works in special cooperation with the Army, treating many of its soldiers and charged with educating its medical corps.

“It’s like a theater of the absurd,” said Prof. Zeev Rotstein, the chief executive officer and director of the hospital. “You have army doctors in white gowns alongside Palestinian doctors who are being trained, at the same time treating Israeli casualties of terrorist attacks and Palestinians who may have been hurt in army actions.”

Yakoub was hurt when Israel bombed an empty, half-ruined Palestinian Interior Ministry building that had been used by Hamas. He was at a wedding party with his family next door. The army said that it had meant to hit the ministry building and that the raid was a response to days of increased rocket fire, mostly aimed at Sderot.

Osher and Rami were hit in the street. They had gone out to buy a birthday present for their father when the rocket crashed down.

Yakoub’s grandmother, Amira Natil, 52, was at the boy’s bedside on Tuesday. She and Yakoub came here with Israeli permission three days after the airstrike from the more basic hospital Al Shifa in Gaza City. “Thank Allah, the lord of the universe,” Mrs. Natil said, kissing her hand and placing it on her brow in a gesture of religious reverence.

Mrs. Natil had not met Osher’s parents and was speaking shortly before they issued their statement, unaware of its contents. About the Israeli boy, she said: “They are children. Haram,” using an Arabic word that denotes something shameful, forbidden or taboo.

Image Osher Twito, 8, of Sderot, in Ashkelon, Israel, before being moved Sunday to Chaim Sheba. Credit... Dan Bality/Associated Press

The story of the Twito brothers has particularly moved Israelis, in large part because of their youth. Osher, described by his family as a keen soccer player, has had his left leg amputated from the knee down. The doctors are still battling to save his right leg. Rami suffered damage to his legs, too. Both boys were transferred to Sheba on Sunday from Barzilai hospital in Ashkelon, a city north of Gaza that has come under rocket fire.