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.
After meeting his cabinet, 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.
Any ceasefire with Hamas had to be permanent, he said, adding that there was international consensus that Palestinian rocket attacks on Israel had to stop.
In particular the hospitals have been depleted and stretched to the maximum because of the closure imposed
Palestinian Authority President Mahmoud Abbas, meanwhile, said he "would not hesitate to stop" peace talks with the Israelis "if they go against our interests and offer a support to aggression".
He called the Israeli bombardment of the Gaza Strip "barbaric and criminal aggression".
Hamas spokesman Ayman Taha told AFP news agency that his group was open to any ceasefire propositions as long as they meant an end to the air strikes and a lifting of the Israeli blockade of Gaza.
The BBC's Middle East editor, Jeremy Bowen, says that if Hamas is open to a ceasefire, it will increase international calls for talks to at least investigate what is possible.
But Israel's leaders are not yet ready to stop their attacks because they need to show that they have won a permanent end to rocket fire from Gaza, adds our correspondent.
Mahmoud Abbas calls for an "honourable truce" in Gaza
International appeals for Israel to end its bombing campaign against Gaza have been mounting.
A European Union statement called for an "unconditional" halt to Hamas rocket attacks.
UK Prime Minister Gordon Brown urged an "immediate and urgent ceasefire" to stem a "humanitarian crisis" in Gaza.
But US President George W Bush repeated earlier statements that Hamas should take the first step to ending hostilities by halting rocket fire into Israel.
White House spokesman Gordon Johndroe said Mr Bush had been assured by Mr Olmert that only Hamas sites in Gaza were being targeted and that "appropriate steps" to avoid civilian casualties were being taken.
While Israeli air raids continued on Wednesday, rockets fired by Palestinian militants landed in and around the southern Israeli town of Beersheba, about 40km (24 miles) from Gaza.
Although no serious casualties were reported, this is the deepest that Palestinian rockets have penetrated inside Israel - something that will only increase Israeli public support for continued military action, observers say.
Hamas rocket reaches Beersheba
A police spokesman said 860,000 Israelis were now in range of Palestinian rockets.
The UN says at least 62 Palestinian women and children have died since Saturday. Palestinian medical officials say more than 1,700 people have been injured, overwhelming Gaza's hospitals.
"In particular the hospitals have been depleted and stretched to the maximum because of the closure imposed," the Red Cross spokesman in Gaza, Iyad Nasr, told the BBC.
It is not known exactly what rockets Hamas and other groups in Gaza have
Israel says Hamas used the six-month truce to boost its arsenal through smuggling tunnels
Grad-style missiles have reached Ashkelon since 2006
Recent strikes in Ashdod could be Iranian-made Oghab, Fajr-3 or Ra'ad missiles
Israel said it was allowing 106 lorries carrying humanitarian aid - including medical supplies - from a variety of international organisations into Gaza on Wednesday.
Israel has massed forces along the boundary with Gaza and has declared the area around it a "closed military zone".
Correspondents say this could be a prelude to ground operations, but could also be intended to build pressure on Hamas.
A statement by Hamas has warned any invasion would see "the children of Gaza collecting the body parts of Israeli soldiers and the ruins of tanks".
The Israeli air strikes began less than a week after the expiry of a six-month-long ceasefire deal with Hamas.
Israel withdrew from Gaza in 2005 but has kept tight control over access in and out of Gaza and its airspace.
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