Mark Regev, spokesman for Ehud Olmert, the Israeli prime minister, said: "We welcome the French-Egyptian initiative. We want to see it succeed," adding that talks would "continue on the basis of that initiative".
"A sustainable calm in the south will be based upon the total absence of hostile fire from Gaza into Israel and an effective arms embargo on Hamas that enjoys international support," he said.
The White House said on Wednesday there was an urgent need to reach a ceasefire agreement in the Gaza conflict between Israel and Hamas, but added that no Franco-Egyptian deal had been accepted.
"We are working to do it as fast as we possibly can," Dana Perino, a White House spokesman, said, adding that the US government still wanted to hear further details about the Franco-Egyptian ceasefire proposal.
Condoleezza Rice, the US secretary of state, has urged Israel to accept the deal, Reuters reported, as discussions continued over the deal at the United Nations in New York on Wednesday.
The Security Council was holding a second day of talks on the crisis in Gaza, with Rice also set to meet Arab foreign ministers at the UN.
Speaking to Al Jazeera from Beirut, Osama Hamdan, a senior Hamas official, said: "The [Hamas] movement is now discussing its stance to the Egyptian initiative, keeping in mind that there are, in principle, a number of reservations on this initiative.
"Israel has not accepted the French-Egyptian initiative yet. They said they are looking positively to this initiative, that does not mean they have accepted it.
"As for the Palestinian Authority, they could accept it but everyone knows that who is on the ground - and can decide 'yes or no' - is the resistance, that means Hamas and the resistance movement. So there is no use in them saying yes or no.
"It is Israel who started the war, not Hamas. When Israel decides to let humanitarian aid into Gaza, it is not a big deal. They have to do that. They are doing this because they are now realising the international anger over the UN school bombing".
Mubarak presented the truce proposal after talks with Sarkozy in the Egyptian resort of Sharm el-Sheikh on Tuesday.
The peace initiative would see an immediate and temporary truce to allow aid into Gaza, measures to prevent arms smuggling from Egypt into Gaza, and for talks.
At least 697 Palestinians have so far been killed and more than 3,085 injured since Israel began its war on the territory.
Amr El-Kahky, Al Jazeera's correspondent on the Egyptian side of Rafah, said Egypt's experience in mediating in the Palestinian-Israeli conflict led them to state their importance in putting forward a proposal.
But Azzam Tamimi, author of Hamas: The Unwritten Chapters, said Egypt had been "a conspirator with Israel" in the war on Gaza, and that was needed today was a much bigger initiative.
"Egypt, geographically, is indispenable, but we need to have Turkey and Qatar in this initiative, for example.
"Qatar has spoken out about the situation in a way that the Arab people understand and has had success in mediating Lebanon's crisis. Turkey is a Nato member, close to Europe and willing to convey the Palestinian perspective."
Israel's ambassador to the UN said on Tuesday that the Israelis were taking the ceasefire proposal "very seriously".
"I am sure that it will be considered and you will find out whether it was accepted," Gabriela Shalev told reporters in New York. "But we take it very, very seriously."
At the same time, Israel's security cabinet is meeting to discuss an escalation to a "third phase" of the war on Gaza, which would see ground combat from street-to-street, according to two senior Israeli political sources.
Hamdan told Al Jazeera that the faction's delegation in Cairo had informed the Egyptian government that any ceasefire would be dependent on some clear conditions on any peace initiative.
"It is not talking about Hamas as a partner, who were elected to govern the Palestinian people. It is not talking about recognising Hamas."
Centre for Strategic Studies in Jordan
"Our delegation [to Cairo] has informed the Egyptian side of our political viewpoint, which is based on the following principles: to immediately end the aggression – and this means an end to all military operations and the withdrawal of the enemy's forces from Gaza – to lift the siege and to open all crossings including Rafah's.
"What is wanted is to end the occupation rather than upholding it through a political process, particularly after this aggression," he said, adding that the "intiatives would protect Israel in the face the Palestinian resistance".
Mohammed al-Masri, a strategic analyst at Jordan University's Centre for Strategic Studies, told Al Jazeera that the initiative had many shortcomings, including the absence of the Israel lifting of the siege.
"It is not talking about Hamas as a partner, who were elected to govern the Palestinian people. It is not talking about recognising Hamas.
Tamimi said the problem with the Egyptian initiative is that it treats Hamas "as if it is not a player".
"But it is the player," he said. "It is fighting Israel and so cannot be ignored as part of the process."