Israel has confirmed Prime Minister Ehud Olmert will meet the Palestinian, Egyptian and Jordanian leaders at a four-way summit in Egypt on Monday.
Mr Mubarak held a peace summit in Sharm el-Sheikh in 2006
An Israeli spokeswoman said the talks would "strengthen the moderates" and "promote Israeli-Palestinian ties".
The announcement came after Palestinian President Mahmoud Abbas described the violent take-over of Gaza by Hamas last week as a bloody coup.
He also accused Hamas of trying to set up its own state in the territory.
A Hamas leader in Lebanon, Osama Hamdan, condemned Mr Abbas's speech as "full of lies".
In the wake of the fighting in Gaza, Mr Abbas - leader of the rival Fatah faction - replaced the national unity government of Prime Minister Ismail Haniya with an emergency cabinet.
Saeb Erekat, a senior adviser to Mr Abbas, said the Palestinian leader would call for a resumption of peace talks with Israel at the summit with Mr Olmert, Mr Mubarak and King Abdullah of Jordan.
"The most important thing to realise is that time is of the essence," Mr Erekat told the Associated Press.
"We need to deliver the end of occupation - a Palestinian state. If we don't have hope, Hamas will export despair to the people."
Earlier, a senior Hamas figure in Gaza said his group wanted to hold talks with Fatah to heal the widening divisions between the Palestinian Territories.
"We think that negotiations with Fatah are the only way out," Sami Abu Zuhri said.