Prime Minister Benjamin Netanyahu warned Palestinian civilians on Sunday to leave immediately any site where militants are operating, one day after Israel flattened a 13-storey apartment block in Gaza.
Israeli aircraft fired a non-explosive rocket at the building as a signal to residents to get out before attacking it on Saturday. Seventeen people were wounded in the strike on the structure, which Israel said had housed a Hamas command centre.
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"I call on the inhabitants of Gaza to evacuate immediately from every site from which Hamas is carrying out terrorist activity. Every one of these places is a target for us," Netanyahu said in public remarks at a cabinet meeting.
With no end in sight to fighting in its seventh week, Netanyahu's tough talk seemed to indicate a move towards bolder strikes against Hamas targets in densely populated neighbourhoods, even at the risk of raising more international alarm.
Hours after Netanyahu spoke, a cluster of 10 homes, one belonging to a Hamas member, was destroyed in an air strike in the southern Gaza town of Khan Younis, neighbours said.
Ten people were wounded by flying debris, but no fatalities were reported. Neighbours said about 10 minutes before the attack, a warning missile was fired and residents fled.
In Gaza City, an Israeli strike on a car killed Mohammed al-Ghoul, described by the Israeli military as a Hamas official responsible for "terror fund transactions".
Ghoul was targeted three days after Israel assassinated three top Hamas commanders in the southern Gaza Strip.
500,000 Gaza residents displaced
In another attack on Sunday, a mother and her four children were killed when their home was bombed in Jabalya refugee camp, hospital officials said. It was not immediately clear why the dwelling was hit, and neighbours said no warning was given.
Militants kept up constant rocket and mortar strikes on southern Israel, wounding three Israelis at the Erez border crossing with the Gaza Strip.
The military said 117 rockets and mortars were launched on Sunday, nine of them intercepted by Israel's Iron Dome system.
'Israel is not ready to talk while under fire.' - Tzipi Livni, Israel's Justice Minister
A mortar attack on the Erez crossing with Gaza wounded four Israelis, and Israel said it had shut the terminal in response for all but emergency cases.
Hamas spokesman Sami Abu Zuhri described Netanyahu's warnings to Gazans to steer clear of potential targets "a clear example of war crimes" against Gaza's civilian population.
Thousands of homes in the Gaza Strip have been destroyed or damaged in the conflict. Nearly 500,000 people have been displaced in the territory of 1.8 million where Palestinians, citing Israeli attacks that have hit schools and mosques, say no place is safe.
Israel has said Hamas bears responsibility for civilian casualties because it operates among non-combatants. The group, it said, uses schools and mosques to store weapons and as launching sites for cross-border rocket attacks.
Palestinian health officials say 2,115 people, most of them civilians and more than 400 of them children, have been killed in the Gaza Strip since July 8, when Israel launched an offensive with the declared aim of ending Palestinian rocket fire into its territory.
Sixty-four Israeli soldiers and four civilians in Israel have been killed. Israel's president attended the funeral on Sunday of a four-year-old boy killed in a mortar bomb attack on Friday.
Gaza school year delayed indefinitely
The bombing on Saturday of Al Zafer Tower in Gaza City marked the first time in the Gaza war that Israel had brought down such a tall structure. It had housed 44 families, some of whom returned to the rubble on Sunday to search for belongings.
Late on Saturday, an Israeli air strike destroyed a commercial centre in the southern Gaza town of Rafah and three people were hurt, local medical staff said.
Egypt called on Israel and the Palestinians on Saturday to halt hostilities and return to talks. But there was no sign that negotiations, last held before a ceasefire collapsed on Tuesday, would resume soon.
Justice Minister Tzipi Livni told Israel's Channel 2 television a ceasefire had to precede any renewed negotiations. "Israel is not ready to talk while under fire," she said, reaffirming Netanyahu's policy.
Livni added that any deal that emerged to halt the fighting also must ensure that "Hamas doesn't reap any achievements," and put the more moderate Palestinian Authority in control of Gaza.
The start of the school year has been delayed indefinitely by the Education Ministry in the Gaza Strip.
Netanyahu said on Sunday that Israelis should be prepared for the war to continue after classes begin on Sept. 1.
Mortar shootings increasing at Israeli communities
But Netanyahu made clear Israel would not open any schools lacking in protection against rocket fire by that date, an official speaking on condition of anonymity said.
With mortar shootings on the rise at Israeli communities near the Gaza border, some Israelis debated whether the area should be evacuated. Israeli media said about a third of border zone residents had sought shelter elsewhere in the country.
Netanyahu told ministers Israel would consider helping anyone leaving a rocket-hit area, but the cabinet avoided broaching any officially sanctioned evacuations fearing that could be seen as a morale booster for Hamas, the official said.
At one UN-run school in Gaza where Palestinian families have been sheltering, children chanting "glory and eternity to our martyrs" stood in line for the national anthem, but no classes were held.
Scott Anderson, Deputy Director of Gaza operations for the United Nations Relief and Works Agency, said although school had been cancelled, some instruction could be provided via television or the Internet.
Hamas has said it would not stop fighting until the Israeli-Egyptian blockade on Gaza is lifted. Both Israel and Egypt view Hamas as a security threat and are demanding guarantees that weapons will not enter the economically-crippled enclave.