Two heavily armed men approached the Israelis, she said, leading an Israeli aircraft to fire a missile at them, killing them. On their backs, she said, were rucksacks apparently holding large amounts of explosives, which caused the nearby house to tumble and kill those inside. She said the analysis was based partly on images taken from the air.

Defense Minister Ehud Barak blamed Hamas. “We see Hamas as responsible for everything that happens there, for all injuries,” he said while on a tour of an Israeli weapons factory, Israeli radio reported. “The army is acting and will continue to act against Hamas, including inside the Gaza Strip.”

The Palestinian Authority in the West Bank, a bitter rival of Hamas, condemned the killing of the mother and her four children. It said in a statement that the Israeli army escalation in Gaza “would harm the efforts to agree on a cease-fire between Israel and the Palestinians.”

After Hamas took over Gaza last June in a battle with forces from Fatah, which now leads the Palestinian government from the West Bank, Israel imposed a blockade on the area, severely limiting supplies into it. Thousands of crude rockets have been launched against southern Israeli towns and communities in recent years by Hamas and smaller factions, which oppose Israel’s existence.

Militants have tried to infiltrate the border crossing into Israel five times in recent weeks. That has led Israel to keep the border closed more often, further reducing supplies and worsening the already severe humanitarian crisis there. Cooking gas has essentially run out since the supplier became too afraid to deliver, Israeli security officials and Gazans say, closing most bakeries.

The United Nations agency that provides the most aid in Gaza suspended its work for four days because of fuel shortages. While United Nations and other international officials complain angrily about Israel’s policies, the attempted infiltrations have recently prompted criticism of Hamas by the European Union, which accused it of actions that “lead to further suffering of the population.”