Israeli Prime Minister Ehud Olmert has said he is ready to meet Palestinian leader Mahmoud Abbas to discuss the stalled Middle East peace process.
Mr Olmert (l) said he did not want to overload Mr Mubarak (r)
However, he did not give any timeframe for the possible meeting.
He indicated he would take unilateral action to fix Israel's borders with the Palestinians, only if the talks failed.
Mr Olmert was speaking in the Egyptian resort of Sharm al-Sheikh, after talks with President Hosni Mubarak, his first with an Arab leader since his election.
BBC Middle East correspondent James Reynolds says the meeting was a summit of introductions, broad statements and flattery - not specifics.
When Mr Olmert was asked whether President Mubarak supported his plan to set Israel's border unilaterally should peace talks with the Palestinians fail, he replied:
"I didn't want to overload the Egyptian president, so we didn't get that far."
Mr Mubarak said repeatedly that he preferred negotiations to be held between Israelis and the Palestinians.
A unilateral withdrawal from parts of the West Bank was a key part of his election campaign, and effectively continues the plan begun by former Prime Minister Ariel Sharon, who remains in a coma since suffering a massive stroke at the start of the year.
Mr Sharon orchestrated a unilateral withdrawal of Israeli troops and settlers from the Gaza Strip in August last year.
Mr Olmert also stressed Israel's commitment to the Middle East peace plan known as the "roadmap".
"My desire [is] to advance this avenue and I intend to meet with chairman Abbas in order to make continuing progress according to the roadmap," he said.
Mr Olmert refuses to meet Hamas, which now runs the Palestinian Authority, accusing it of being a terrorist group.
Mr Abbas is not from Hamas but the Fatah movement of Yasser Arafat, which was roundly defeated in January elections.
With the Palestinian economy in crisis after donors withdrew funding from the Hamas-led authority, Mr Olmert said he would not stop Egypt from delivering humanitarian aid across the border to Gaza.
"We will take all steps to prevent a humanitarian disaster in the Gaza Strip," he said.
On Sunday some Palestinian civil servants were paid for the first time in three months.
Mr Olmert, who was elected in March, visited Washington last month for talks with US President George W Bush and is expected to head to Europe soon.
The meeting with Mr Mubarak comes two days after the Israeli army killed two armed men in Egyptian uniform on the Israeli-Egyptian border - a frontier which is normally very quiet.
Mr Olmert expressed regret for the incident and said there would be a joint investigation.