Both sides rejected any notion of a ceasefire soon, three days after Israeli leaders launched bombing raids with the declared aim of halting rocket salvoes from the Hamas-controlled coastal enclave.
"None of us can say how long it will take," Israeli President Shimon Peres said after being briefed at the Defence Ministry.
Defence Minister Ehud Barak said Israel, which is blockading Gaza, was gathering ground forces at the frontier and would expand its operation "as much as is necessary" to stop the rocket fire and "deal a heavy blow to Hamas".
Despite winter rain - weather that could impede any ground incursions - Israeli warplanes pressed on for the fourth day with attacks on Hamas targets, killing 12 Palestinians. They included sisters aged four and 11.
Hamas seized control of the Gaza Strip from Palestinian President Mahmoud Abbas's Fatah faction in fighting in June 2007. It has rejected international demands to recognise Israel, renounce violence and accept existing interim peace deals.
Mushir al-Masri, a Hamas official, said: "We are not begging for calm and there is no room to talk about calm amid the continued aggression and siege."
Rockets fired from the Gaza Strip struck outside the Israeli towns of Kiryat Malachi and Rahat, a bedouin community near the southern city of Beersheba, areas some 18 miles from the territory and which had not been attacked before.
There were no reports of casualties after the salvoes, a day after three Israelis were killed by rockets.
Medical officials put Palestinian casualties since Saturday at 383 dead and more than 800 wounded. A United Nations agency said at least 62 of the dead were civilians. In all, four Israelis have been killed since the operation began.
"We are living in horror, we and our children. The situation is not just bad, it is tragic," said Gaza resident Abu Fares, standing outside his home, near the rubble of a building that was bombed and destroyed overnight.
Israeli media quoted Prime Minister Ehud Olmert as saying the Gaza operation, launched by his centrist government six weeks before a national election that opinion polls predict the right-wing Likud party will win, was in "the first of a several stages".
Likud leader Benjamin Netanyahu, saying he had answered Olmert's call to "help out in Israel's PR (public relations) efforts", told Reuters the Jewish state would eventually have to remove Hamas from power in the Gaza Strip.
"Whether it can be done right now is something I don't think we should discuss here. But it should be discussed because ultimately, if we don't do it, then Hamas will rearm itself," he said.
The United Nations and the European Union's executive arm have called for an immediate truce. But Israeli Interior Minister Meir Sheetrit said "there is no room for a ceasefire" with Hamas until the threat of rocket fire had been removed.
The Israeli military "has made preparations for long weeks of action," added Matan Vilnai, a deputy defence minister, in broadcast remarks.
In Beit Hanoun, in the northern Gaza Strip, two sisters were killed in a air raid as they were taking out the trash near their home, medical workers said. The area has been a launching ground for cross-border rocket attacks.
Later a security man was killed in a strike on a headquarters in Khan Yunis and Israeli missiles flattened five ministerial buildings and a structure belonging to the Islamic University in Gaza City.
A Hamas sports centre and two training camps belonging to the group were also destroyed in the attacks, which plunged Gaza into a blackout as explosions echoed across the city.
Israeli aircraft fired missiles at the home of a senior commander in Hamas's armed wing. He was not home. Another attack targeted offices belonging to the Popular Resistance Committees militant group.
In Ashdod, an Israeli woman bolted from her car to seek shelter after a siren sounded, but she tripped and fell in the street, where she was killed by a rocket, local officials said.
Israel kept schools closed within a radius of about 18 miles from the Gaza border, citing concerns about further rocket fire. Residents were told to remain indoors and on the alert for alarms heralding incoming rockets.
Most Gazans in the territory of 1.5 million people, one of the most densely populated on earth, have stayed home, in rooms away from windows that could shatter in blasts from air strikes on Hamas facilities.
Israel declared areas around the Gaza Strip a "closed military zone", citing the risk from Palestinian rockets, and ordered out journalists observing a build-up of armoured forces.
Israel has said it would allow more aid trucks into Gaza. Dozens of trucks loaded with goods were seen heading to Gaza crossings early on Tuesday.
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