Arab foreign ministers are due to meet in Cairo on Wednesday to discuss calling an emergency region-wide summit on the crisis.
"If you think that Hamas and al-Qassam will be crushed, we will rise up from the rubble"
spokesman Ezzedine al-Qassam Brigades
On the ground however there is little sign of an end to hostilities, with Israeli jets continuing to pound Gaza, adding to the misery of civilians trapped in the densely-populated strip, much of which is without power and with food supplies running dangerously low.
Early on Wednesday a Palestinian medic was killed when his ambulance was hit by an Israeli missile.
Witnesses reported missiles also hitting Hamas positions in Gaza city as well as the network of tunnels under the Gaza-Egypt border.
The latest attacks followed a statement issued by the armed wing of Hamas warned that it would step up rocket attacks against Israel.
"We tell the leaders of the enemy - if you continue with your assault, we will hit with our rockets further than the cities we have hit so far," a masked spokesman for Ezzedine al-Qassam Brigades said in a televised statement.
"If you think that Hamas and al-Qassam will be crushed, we will rise up from the rubble," the spokesman, named as Abu Obaida, said.
Tuesday saw a barrage of more than 40 rockets fired from Gaza into Israel, many striking deeper than before.
'No room for ceasefire'
The Hamas statement came amid warnings from Israel that the onslaught on the Gaza Strip could last for "weeks", with the country's defence minister, saying stronger action may be yet to come.
"We are ready to deepen and widen the operation in order to make sure that the calm and tranquillity will come back to the region," Ehud Barak said.
"We believe that this is our primal contract with our citizens to protect them against terrorist attacks."
His comments were echoed by Israel's interior minister who said there would be no let up until the threat of Palestinian rockets attacks from the Gaza Strip had been removed.
"There is no room for a ceasefire," Meir Sheetrit told reporters.
He added that the Israeli military would not stop its operations "before breaking the will of Palestinians, of Hamas, to continue to fire at Israel."
In Gaza more than 380 people have been killed, including at least 61 women and childrena as a result of the Israeli bombardment nd local hospitals are saying they are unable to cope with any more casualties.
In the same period four Israeli citizens have been killed by rockets fired from Palestinian positions.
'Lasting and durable'
"We are ready to deepen and widen the operation in order to make sure that the calm and tranquility will come back to the region"
Israeli defence minister
In the US, the Bush administration continued to give its tacit backing to the Israeli strikes, saying it was up to Hamas to give sufficient assurances that any ceasefire would hold.
"We have got to get a commitment from Hamas that they would respect any ceasefire and make it lasting and durable," White House spokesman Gordon Johndroe told reporters.
"So until we can get that assurance - not the United States, but until Israel can get that assurance from Hamas - then we're not going to have a ceasefire that is worth the paper it's written on."
He added that all sides wanted to see an end to the violence, "but that first starts with Hamas ceasing its rocket attacks into Israel."
Israel's military meanwhile has been massing infantry and armoured forces along the border with Gaza, increasing speculation that a ground invasion is planned
|Israel says its ground forces are ready to act if it decides to enter Gaza [EPA]
On Monday, areas of the border were declared "closed military zones" and thousands of reservists have been called up by the Israeli military.
"The ground forces are ready," Avital Leibovitz, an Israeli military spokeswoman, said on Tuesday.
"The option exists. It is possible that we will apply it but for the moment we are only hitting from the air and the sea."
Mark Regev, an Israeli government spokesman, told Al Jazeera that the Israel military was was being "as surgical as it can be", while Hamas rocket attacks indiscriminately targeted civilians.
"We have been hitting Hamas command-and-control, Hamas military structures ... our target is not the innocent people of Gaza, it is only the Hamas military machine," he said.
"Our feeling towards the people of Gaza is not hostility, we see them as victims of the terrible Hamas Taliban-type regime, just as the people of southern Israel are victims."