“Look at where they have forced us to live,” said Mr. Hillis’s wife, Insaf, in the family’s tent behind the hospital. “Every family here has a son or a father or a brother who has been killed, and all of their children will grow up wanting revenge.”

“The rockets don’t protect us, and the Jews’ tanks and jets don’t protect them,” he said. “The only thing that could protect us would be peace between us.”

GAZA CITY — When artillery shattered their home near the Israeli border, Ibrahim Hillis, a grandfather, rushed his extended family to the city to seek shelter, but the schools were full and relatives’ houses were already packed with others displaced by the war.

So home became a patch of thin grass around a tree trunk behind this city’s central hospital, where his family rigged up sheets to block the sun. Scores of other families had done the same, food and water were scarce, and ambulances bearing the victims of new attacks screamed in day and night.

“We are living in the dirt,” said Mr. Hillis, 73. “There is no work, no money, no medical treatment, and everything is decided by those fighting, so what can we, the people, do about it?”

Three weeks of war between Israel and Palestinian militants in Gaza have pushed the territory to the brink of humanitarian disaster. Israel’s military on Tuesday broadened its offensive, bombing 150 sites, and one strike set ablaze the territory’s only power plant, filling the sky with smoke and cutting the electricity needed to pump water and sewage systems as well.