Bernard Kouchner, the French foreign minister, made two telephone calls to Ehud Barak, the Israeli defence minister, on Tuesday appealing to him to consider the truce, two senior officials in Barak's office said.
However, Yigal Palmor, a foreign ministry spokesman, said it was unrealistic to expect Israel to agree to a plan "with no mechanism to enforce the cessation of shooting and terror from Hamas".
Israel has, so far, said it will refuse to enter into a new ceasefire with Hamas until rocket and mortar attacks by Palestinian fighters were halted.
Four Israeli citizens have been killed in such attacks since the Israeli offensive began on Saturday.
The European Union added it voice to calls from the United Nations Security Council and the Middle East "Quartet" to end to the violence.
"There must be an unconditional halt to rocket attacks by Hamas on Israel and an end to Israeli military action," an EU statement said.
"There is no military solution to the Israeli-Palestinian conflict, in Gaza or elsewhere."
Ehud Olmert, the Israeli prime minister, reportedly discussed the French proposal with his foreign and defence ministers on Tuesday night, but his office said details of the meeting would not be released.
The discussions focused on "diplomatic, military and operational aspects of Israel's next steps," his office said.
Al Jazeera's Alan Fisher, reporting from the Israeli-Gaza border, said there was a real possiblity the truce could be approved.
"They will decide whether or not Hamas has been weakened enough to allow this to go ahead, he said.
"It will play well with the international community if Israel does stop the violence, and if Hamas does break the ceasefire then Israel can launch a ground war saying 'we tried to give peace a chance but Hamas didn't want it.'"
There was little sign of an end to hostilities on the ground, with Israeli jets hitting Gaza for a fifth day, adding to the misery of civilians trapped in the densely-populated strip, much of which is without power as food supplies run dangerously low.
"If they [the Israelis] halt the aggression and the blockade, then Hamas will study these suggestions"
Early on Wednesday a Palestinian medic was killed when his ambulance was hit by an Israeli missile.
Witnesses reported other missiles hitting Hamas positions in Gaza city as well as the network of tunnels used for smuggling both basic supplies and weapons under the Gaza-Egypt border.
Mushir Masri, a Hamas spokesman, said any halt to rocket and attacks on southern Israel would require an end to Israel's crippling blockade of the Gaza Strip.
"If they halt the aggression and the blockade, then Hamas will study these suggestions," he said.
Israel has maintained a blockade of the Gaza Strip since Hamas took full control in 2007, restricting supplies of basic neccesities, fuel and medicine.
The armed wing of the Palestinian movement warned that it would step up rocket attacks against Israel if the bombardment was not ended.
"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 Izz-e-din al-Qassam Brigades said in a televised statement.
|Israel has previously said it will not accept a truce unless rocket attacks stop [AFP]
"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.
The Hamas statement came amid warnings from Israel that the onslaught on the Gaza Strip could last for "weeks".
In the US, the Bush administration continued to give its tacit backing to the Israeli raids, 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," Gordon Johndroe, a White House spokesman, 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.
Arab foreign ministers were due to meet in Cairo on Wednesday to discuss calling an emergency region-wide summit on the crisis.