In an interview published on Friday, Egypt's leading pro-government newspaper, Al-Ahram, quoted Mubarak as saying:"Egyptian contacts with several Hamas leaders resulted in preliminary, positive results in the shape of a conditional agreement to hand over the Israeli soldier as soon as possible to avoid an escalation.
"But agreement on this has not yet been reached with the Israeli side," Mubarak said.
The president said that he had asked Ehud Olmert, the Israeli prime minister, "not to hurry" the military offensive in Gaza, but to "give additional time to find a peaceful solution to the problem of the kidnapped soldier".
Israel suspended a planned ground invasion of northern Gaza on Thursday, giving diplomacy another chance to free the Israeli soldier, Corporal Gilad Shalit, whom fighters linked to Hamas captured on Sunday from an Israeli camp near Gaza.
Mubarak's remark implied that he was claiming a role in Israel's decision.
Meanwhile, witnesses have said that Israeli warplanes hit offices of the Fatah movement and a Hamas facility in Gaza City early on Friday. There were no reports of casualties.
The military had no immediate comment. The air strikes followed an attack on the Palestinian interior ministry in Gaza City, among more than a dozen air attacks by Israeli forces in the Gaza Strip in the past few hours.
However, in Jerusalem, Gideon Meir, a senior Israeli foreign ministry official, said Israel did not know of such an offer.
Reached just after midnight on Friday morning, Meir told The Associated Press that Israel would have no comment until daybreak.
"In general, Israel's stance is, as the prime minister said earlier, that the soldier will only be released unconditionally and there will be no negotiations with a gang of terrorists and criminals who abducted a soldier from Israeli territory"
Gideon Meir, senior Israeli foreign ministry official
"In general, Israel's stance is, as the prime minister said earlier, that the soldier will only be released unconditionally and there will be no negotiations with a gang of terrorists and criminals who abducted a soldier from Israeli territory," Meir said.
Hamas leaders in Gaza were not answering their phones early on Friday.
"Israeli leaders promised, and I hope they will stick to it, not to shed the blood of innocent Palestinian civilians in any hurried military operation," Mubarak said.
"At the same time, Egypt warned Hamas leaders of the dire consequences of adopting of tough positions and urged them to shoulder their responsibilities in view of the dangers and difficulties faced by the Palestinian people at the present time," Mubarak said.
In a bid to force the release of the soldier on Wednesday, Israeli aircraft blasted two bridges and a power station in Gaza, cutting off electricity for the southern part of the territory, and deployed tanks and thousands of troops near the southern town of Rafah.
Israeli aircraft and artillery hit
sites across Gaza
On Thursday, Israeli aircraft and artillery pounded sites across Gaza, hitting suspected weapons factories, an electrical transformer and militant training camps.
No deaths or serious injuries have been reported since the operation began.