Sarkozy said that Mubarak had invited “the Israeli side to come and discuss the matter of border security, without delay, and perhaps in the hours to come."
Sarkozy also said that he had spoken to Ehud Olmert, the Israeli prime minister, about Mubarak's initiative and "he will react soon."
"I have very precise elements that allow me to say that an Israeli delegation will meet an Egyptian delegation to discuss the matter of security," Sarkozy said.
Earlier on Tuesday, Sarkozy called on Syria to help convince Hamas to co-operate in international efforts to end the Israeli assault in the Gaza Strip during talks with Bashar Al-Assad in Damascus.
Sarkozy told the Syrian president that he "didn't have any doubt" that Syria would help convince Hamas to agree to a deal.
Sarkozy said: "I know the importance of Syria in this region and its influence on a number of players.
"I don't have any doubt that President Bashar Al-Assad will throw all his weight to convince every one to return to reason. Those who can work for peace must do it immediately."
Syria, along with Iran, is a main backer of Hamas and hosts members of the group's exiled leadership, including Khaled Meshaal, Hamas' leader.
Truce 'not far'
Following the trip to Syria, Sarkozy visited French United Nations peacekeepers in south Lebanon and said that a deal to end the Israeli offensive in Gaza was "not far" away.
He said: "I'm convinced that there are solutions. We are not far from that. What is needed is simply for one of the players to start for things to go in the right direction."
The president had said on Monday that he was working on an intitiative with Egypt but declined to give details because of "extremely complex negotiations".
During Sarkozy's visit to Syria, Al-Assad said that any initiative for a truce must stop what he described as Israel's war crimes in Gaza and lift the blockade in the besieged territory.
Al-Assad said "We have only a few hours between one massacre and the other being perpetrated and carried out in the Palestinian territories.
"And we don't have days or weeks. Unless the situation is remedied swiftly we will face a very dire situation."
"We have to immediately stop the barbaric Israeli aggression in Gaza. Thirty percent of the victims are children under the age of ten and Gaza is now a concentration camp."
Diplomats in the Syrian capital said that France wanted Syria to exert its influence with Hamas to make sure that any ceasefire sticks, but Syria has been careful not to be seen as acting as a guardian of Israel's security.
Sarkozy's peace-brokering mission in the region is just one of many diplomatic efforts around the world aimed at ending the Israeli offensive in the Gaza Strip.
|Erdogan said Israel's leaders were leaving a 'black stain... on humanity' [EPA]
Recep Tayyip Erdogan, Turkey's prime minister, has completed a week-long tour to Syria, Jordan, Egypt and Saudia Arabia, in which he outlined a two-stage proposal to end the conflict.
The proposed agreement would secure a ceasefire between Israel and Hamas and
then work to end the division of the Palestinians.
Erdogan condemned Israel's offensive as "savagery" on Tuesday and said it was a bid by the Israeli leadership to score points ahead of general elections in February.
Referring to the Israeli ministers of defence and foreign affairs, Erdogan said: "I am telling Ehud Barak and (Tzipi) Livni to forget about the elections, because history will judge them for the black stain they are leaving on humanity."
Israel "has suffered much in history and should know best the sanctity of human life, especially that of women and children... and the importance of the culture of co-existence".
Tony Blair, the Middle East envoy for the Quartet comprising the United Nations, the European Union, Russia and the United States, has met with several Israeli and Palestinian officials in recent days, and has called on Hamas to work towards a ceasefire to stop the "appalling suffering" in Gaza.
The former British prime minister said that the international community wanted dialogue with Hamas, but they had to end violence first.
Speaking to BBC radio in Jerusalem, he said: "There are circumstances in which we could get an immediate ceasefire."
"Those circumstances focus very much around clear action to cut off the supply of arms and money through the tunnels that go from Egypt into Gaza.
"The Egyptians, in principle, are prepared to do this, they want to do it, they recognise it's in their own interests as well".
Israel rejected European proposals for a ceasefire and the deployment of international observers following talks on Monday with a high-level EU delegation in Jerusalem.
Mahmoud Abbas, the Palestinian president, will address the UN Security Council in New York later on Tuesday, but as diplomatic efforts continue UN staff on the ground say time is running out.
They say Gazans have little food and water left and that the injured are dying because of the lack of medicine.