The Hamas PM's offices were again attacked early on Wednesday
The UN Security Council has discussed a draft resolution calling for an immediate ceasefire to halt the Israeli-Palestinian violence.
But the meeting failed to vote on the Libyan draft after ambassadors from the US and UK said it contained nothing about Palestinian attacks on Israel.
The draft condemned Israel's military action and called on it to cease.
Earlier, Israeli PM Ehud Olmert rejected calls for a 48-hour truce to allow more humanitarian aid into Gaza.
In New York, the Palestinian envoy to the UN, Rijad Mansour, demanded a binding resolution to secure an immediate truce.
But the Israeli ambassador, Gabriela Shalev, said her country would continue to do whatever necessary to protect itself against what she called terrorism.
The US ambassador at the UN - who as one of the permanent Security Council members can veto any resolution - said that he believed it was up to Israel and Hamas themselves to agree to a ceasefire, and that the UN should not impose one.
France's President Nicolas Sarkozy has said he would visit the region in a bid to end the crisis, which has seen five days of Israeli raids and Hamas rocket fire.
But Palestinian President Mahmoud Abbas has threatened to pull out of peace talks.
He called the Israeli bombardment of Gaza "barbaric and criminal aggression" and said he "would not hesitate to stop" peace talks with the Israelis "if they go against our interests and offer a support to aggression".
After meeting his cabinet on Wednesday, Prime Minister Olmert said conditions were not right for a ceasefire, but he did not rule one out in the future.
"If conditions will ripen, and we think there can be a diplomatic solution that will ensure a better security reality in the south, we will consider it. But at the moment, it's not there," he was quoted by aides as telling the cabinet.
"We did not launch the Gaza operation only to end it with the same rocket firing that we had at its start," Mr Olmert said.
In the last five days, Israeli jets and attack helicopters have hit Hamas targets, including security compounds, government buildings, smuggling tunnels under the border with Egypt and homes belonging to militant leaders.
Palestinian officials say 391 Palestinians have died in the Israeli air strikes; four Israelis have been killed by rockets fired from Gaza, which is under Hamas control.
Gaza wakes up to another day of air strikes
The southern Israeli town of Beersheba was hit, the deepest penetration by rockets so far.
International calls have been mounting for both sides to call off the attacks as hospitals in Gaza struggle to cope with the scale of the casualties and supplies of food and fuel run low.
The UN Security Council meeting on the eve of the new year was convened at the request of the Arab League.
Arab League foreign ministers meeting in Cairo want a binding UN resolution to ensure an immediate ceasefire in Gaza and a lifting of the Israeli blockade of the territory.
France's President Sarkozy said he would travel to the Middle East on Monday because "France's duty was to look everywhere for the roadmap towards peace".
He will first meet Israeli Foreign Minister Tzipi Livni in Paris on Thursday.
Israel has massed forces along the boundary with Gaza and has declared the area around it a "closed military zone" leading to speculation a ground offensive into the tiny coastal strip could be imminent.
"Our people will defeat those tanks," said the Hamas leader in Gaza, Ismail Haniya, adding that Hamas would only discuss a ceasefire if Israel first stopped its bombing.
"If the aggression is halted unconditionally and the blockade is lifted and the [border] passages are opened, we then can discuss all issues in a positive manner," he said in a televised address.
US President George W Bush repeated his earlier statement that the onus was on Hamas to take the first step to ending hostilities by halting rocket fire into Israel.
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