Mr Netanyahu has avoided going into detail about he plans to clinch peace
Israeli PM Benjamin Netanyahu has said wants Israelis and Palestinians to live in peace, security, and prosperity.
After talks in Egypt with Hosni Mubarak, he added that he wanted peace talks to resume as soon as possible.
Relations between Israel and its oldest Arab ally have been tense since Mr Netanyahu became prime minister heading a mainly right-wing government.
Egypt is concerned about its approach to peace with the Palestinians and its foreign minister, Avigdor Lieberman.
The BBC's Yolande Knell says there is deep concern in Cairo that the Israeli government has so far refused to endorse the idea of the creation of a Palestinian state.
to clarify his position on what many, including the current US admistration, see as bedrock policy for international diplomacy in the Middle East.
Israeli Foreign Minister
is not expected to accompany Mr Netanyahu on his trip to Egypt.
In 2008, Avigdor Lieberman said Mr Mubarak could "go to hell" for refusing to visit Israel. His appointment has put strain on bilateral relations.
'Talks within weeks'
Mr Netanyahu arrived at the resort town of Sharm el-Sheikh earlier on Monday. It was his first foreign trip since taking office on 1 April.
"We would like to resume as soon as possible the peace talks between us and the Palestinians, and I hope they will be renewed in the coming weeks," he said at a joint news conference with the Egyptian leader after talks.
"We would like to extend peace first of all with our Palestinian neighbours. We would like Israel and the Palestinians to live with prospects of peace, security and prosperity. The three things go together and not one at the expense of the other."
Mr Mubarak said he had pressed the Israeli prime minister to endorse the principle of a Palestinian state.
"The prime minister stressed his government's commitment for peace... and for my part I stressed Egypt's aspiration for positive positions which reflect his commitment for peace... through a two-state solution," Mr Mubarak said.
Israeli officials said ahead of the talks that Mr Netanyahu would try to secure Egyptian support for its campaign to halt Iran's nuclear drive, which Israeli leaders characterise as the main threat to their state.
Both Mr Netanyahu and Mr Mubarak are due to head to Washington to meet President Barack Obama soon.
Mr Obama has promised to vigorously pursue peacemaking in this region.