More than six hours later, there was still no official comment about the strike from the Israeli military, which continued to withdraw many of its ground forces from populated areas in Gaza, about why it struck the house.

After sharp criticism from the United States and the United Nations of its strike outside a United Nations school on Sunday, which killed seven people in addition to its intended targets, three Islamic Jihad fighters on a motorcycle, Israel announced a unilateral cease-fire to last from 10 a.m. until 5 p.m. Israel said the cease-fire was intended to assist humanitarian relief efforts.

But the cease-fire was to take place only in areas where Israel was not engaged in military activity. Israeli Army officials said that east Rafah, in southern Gaza, far from Gaza City itself, was the only urban area where troops and tanks were engaged in fighting on Monday, with most of the rest of the Israeli troops pulled back closer to the border with Israel and some redeployed in staging areas inside Israel itself.

Gen. Motti Almoz, the chief military spokesman, told Army Radio that “redeployment lets us work on the tunnels, provides defense and lets the forces set up for further activity.”

“There is no ending here, perhaps an interim phase,” he said.

Sami Abu Zuhri, a spokesman for Hamas, the dominant faction in Gaza, said it would not observe the truce, which he disparaged as a media exercise, and he warned residents to exercise caution when they ventured outside. “The unilateral cease-fire announced by Israel is an attempt to divert attention from Israeli massacres,” he said. Earlier Monday, Israel bombed the house of an Islamic Jihad commander in northern Gaza, Danyal Mansour, killing him.

Ashraf al-Qedra, a spokesman for the Health Ministry in Gaza, said that the strike on the house in Shati took place several minutes after the announced start of the cease-fire, but one Israeli official from the army agency that controls coordination with Gaza told Israel Radio that the strike took place just before the cease-fire began.

The cease-fire, coupled with the redeployment, was another indication of Israel’s decision for now to reject further negotiations on a cease-fire with Hamas or with President Mahmoud Abbas of the Palestinian Authority, and instead to make unilateral decisions. After a string of broken cease-fires, the Israeli intention, officials explained, was not to reward Hamas and allies like Islamic Jihad through negotiated concessions, but to wait and see whether the armed groups in Gaza, badly damaged by this conflict, will stop attacking Israel.

The last major Israeli war in Gaza ended after three weeks with a unilateral Israeli cease-fire in January 2009, which took hold after a few days. A briefer conflict, in November 2012, ended with negotiations carried out by the Egyptian president at the time, Mohamed Morsi of the Muslim Brotherhood, who saw Hamas as an ally. But the deal arranged then to ease restrictions on Gaza in return for “quiet” did not last, and Israel does not trust Hamas to implement any negotiated arrangement.

At the same time, Israeli officials argue, Egypt’s new president, Abdel Fattah el-Sisi, the military man who ousted Mr. Morsi, sees the Muslim Brotherhood and Hamas as a threat to Egypt, a position of antagonism to Hamas even sharper than Egypt’s position under Hosni Mubarak during his three decades in power.

Egypt now, having largely halted the tunnel trade in smuggled goods and arms that flourished under both Mr. Mubarak and Mr. Morsi, will make it much harder for Hamas and its allies to resupply themselves with weaponry and building materials for new tunnels.

At the same time, with its control of the Rafah crossing, Egypt has great leverage over Gaza, and one idea is to try to empower Mr. Abbas and the Palestinian Authority, which is still dominated by the Fatah faction, to take responsibility with Egypt over the crossing.

In Cairo, Palestinian factions were working on a joint position, demanding that for a cease-fire, Israel pull all its troops from Gaza, loosen its controls over goods and people entering and exiting Gaza, and open border crossings.

But for the moment, at least, Israel has decided not to negotiate, and even a senior American diplomat who went to Cairo for the talks has left the city.

In East Jerusalem, the police shot and killed a local Palestinian who drove a construction vehicle over a pedestrian, killing him, and then knocked over a bus, which happened to be nearly empty, slightly injuring three people. The incident took place in an ultra-Orthodox Jewish neighborhood, and the police said that they were regarding the attack as a response to Israel’s conflict in Gaza. Tensions have been high in Jerusalem and in the West Bank, with intermittently violent protests against Israeli policies and war conduct.