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Israel has dropped leaflets on the Gaza Strip warning residents that it is to escalate its military action.
There is speculation the leaflets may mean Israel will adopt new tactics in its battle with Palestinian militants.
On Saturday, Israel attacked dozens of Hamas targets, including what it says were rocket-launching sites, weapons stores, and smuggling tunnels.
Israel said Hamas militants fired more than 30 rockets across the border, injuring two Israelis in Ashkelon.
Medical staff in Gaza say more than 800 Palestinians have died during the two-week offensive. Thirteen Israelis have been killed, most of them troops.
Leaflets and phone messages in Arabic urged Gaza residents to keep away from sites linked to Hamas, saying that the Israeli Defense Forces (IDF) were not targeting Gazans but "Hamas and the terrorists only".
One phone message said "the third stage" of the operation would start soon. It is two weeks since air strikes on Gaza began. The ground attacks started a week ago.
Correspondents say phase three could see Israeli forces moving deeper into cities and refugee camps - involving new risks for Israeli soldiers and civilians in the Gaza Strip.
In the bloodiest incident so far on Saturday, eight people who appeared to be civilians were killed when an Israeli tank shell hit a street in Jabaliya, Palestinian medical officials said.
The BBC's Hamada Abuqammar in Gaza says Red Cross workers rescued 13 women and children in the north of the Strip, but were prevented from recovering bodies by the IDF.
Israel said it launched more than 70 attacks on Hamas targets on Saturday by air, land and sea, "hitting armed terror operatives in different incidents".
An Israeli army spokesman said a senior Hamas militant involved in rocket-launching in the Gaza City area, Amir Mansi, was among those killed. There has been no word from Hamas.
These figures could not be independently confirmed. Israel is preventing international journalists from entering the coastal strip.
On the ground, Israeli troops are reported to have moved closer to the edge of Gaza City, though they have yet to go into the most densely populated areas.
Hamas fired more rockets at Israel, injuring two Israelis in the town of Ashkelon, the Israeli military said. It follows more than 30 missiles attacks from Gaza the previous day, it said.
The continued violence comes as rival Palestinian groups converged on Cairo for discussions about an Egyptian ceasefire initiative, which is also sponsored by France.
Palestinian Authority President Mahmoud Abbas urged all sides to accept the proposal "without delay", after meeting Egyptian President Hosni Mubarak in Cairo.
But Mr Abbas - who heads the secular Fatah movement, bitter rivals of Hamas - does not control Gaza, and analysts say he will have little impact on the course of the conflict.
Hamas, which took control of Gaza in June 2007, has sent delegates to Cairo for the second time in a week for separate talks.
Egypt negotiated the last ceasefire between Hamas and Israel but, correspondents say, this conflict has strained an already difficult relationship between Cairo and Hamas.
Israel and Hamas have ignored a UN Security Council call for an immediate ceasefire that would lead to the withdrawal of Israeli troops.
Israel said the continued rocket attacks showed the resolution was "unworkable", while Hamas insisted any truce must include the ending of Israel's economic blockade of Gaza.
Aid agencies say Gaza's 1.5 million residents are in urgent need of food and medical aid.
The UN says it has resumed aid deliveries in Gaza after suspending operations on Thursday when it said the driver of one of its lorries was killed by Israeli fire.
The IDF said it was "100% certain" it did not attack the vehicle.
The violence erupted as a six-month truce between Israel and Hamas unravelled in November and comes one month before a parliamentary election in Israel.