The two leaders spoke for 90 minutes
The Israeli Prime Minister, Benjamin Netanyahu, has met Egypt's president ahead of the expected resumption of indirect Middle East peace talks.
Mr Netanyahu and Hosni Mubarak spoke for 90 minutes in the Egyptian Red Sea resort of Sharm el-Sheikh.
An Israeli government statement said the talks had been "constructive" and had taken place "in a good atmosphere".
Mr Netanyahu later discussed the peace efforts with US President Barack Obama in a telephone call, officials said.
It came as the US envoy, George Mitchell, returned to the region.
The Palestinian Authority has refused to attend the indirect "proximity talks" mediated by Mr Mitchell since March, when Israel approved plans for the construction of 1,600 homes in a settlement in East Jerusalem.
'Preparing the ground'
During their meeting on Monday, Mr Netanyahu and Mr Mubarak "reviewed Egyptian and international efforts to prepare the ground for the indirect talks aimed at a two-state solution," the Egyptian news agency Mena said.
The Israeli prime minister's office said they had discussed "renewing the peace process and other regional and bilateral issues".
Israeli media reports say the proximity talks will resume on Wednesday.
However, Palestinian leaders are said to require the backing of the Palestine Liberation Organisation (PLO), which will not meet until Saturday.
Israeli-Palestinian peace talks have been stalled since 2008.
Israel has occupied the West Bank, including East Jerusalem, since 1967. It insists Jerusalem will remain its undivided capital.
Nearly half a million Jews live in more than 100 settlements in the West Bank, among a Palestinian population of about 2.5 million.
The settlements are illegal under international law, although Israel disputes this.
The Palestinian Authority has refused to enter direct talks unless Israel completely halts building in the West Bank and East Jerusalem.
In November, Israel announced a 10-month suspension of new building in the West Bank, under heavy US pressure. But it considers areas within the Jerusalem municipality as its territory and thus not subject to the restrictions.
But reports suggest an unofficial slowdown of approvals for major projects in East Jerusalem may have been instigated by Mr Netanyahu in an attempt to help mend relations with the US strained by March's announcement.