Israeli forces quoted by AFP news agency said at least 550 militants had been killed so far. Thirteen Israelis have died in the conflict, most of them soldiers.
The Hamas leader-in-exile, Khaled Meshaal, condemned the Israeli offensive as a "holocaust", in a speech broadcast to millions across the Arab world via al-Jazeera TV.
From his base in Syria, he said Israel had "finished off the last chance" for compromise and settlement, and that the war in Gaza had brought resistance to every Palestinian household.
The conflict has sparked worldwide anti-war demonstrations, with tens of thousands of people joining rallies on Saturday in the US, Europe and the Middle East.
In Gaza, leaflets and phone messages in Arabic urged 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 what appeared to be the bloodiest incident on Saturday, Palestinian medical staff said eight Palestinian civilians were killed by Israeli fire in Jabaliya - a claim later denied by the Israeli army.
Israel said it had launched more than 70 attacks on Hamas targets by air, land and sea, "hitting armed terror operatives in different incidents".
An Israeli army spokesman said the commander of the Hamas' rocket-launching squads in Gaza City, Amir Mansi, was among those killed.
There has been no word from Hamas, but militants continued to fire rockets into Israel.
Israel is preventing international journalists from entering the coastal strip, and none of the figures could not be independently confirmed.
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.
The continued violence comes as rival Palestinian groups converged on Cairo for discussions about an Egyptian ceasefire initiative, which is also sponsored by France.
Israeli strike 'kills family of eight'
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 was elected in 2006 and took control of Gaza in June the following year, has sent delegates to Cairo for the second time in a week for separate talks.
From Damascus, Khaled Meshaal said a breakthrough would come only if Israel immediately stopped the bombardment, lifted the blockade of Gaza, opened all crossings and withdrew its troops.
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.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.