Egypt has been regularly involved in Middle East diplomacy
Israeli President Shimon Peres has been meeting his Egyptian counterpart Hosni Mubarak for talks on Middle East peace.
The pair were expected to discuss Israeli-Arab peace plans, the fate of Israeli soldier Gilad Shalit and Israel's ceasefire with the Gaza Strip.
Egypt has been brokering a potential prisoner exchange between Israel and the leaders of the Palestinian Hamas movement, which runs the Gaza Strip.
The two leaders met at the Red Sea resort of Sharm el-Sheikh.
Shimon Peres holds a largely ceremonial role in Israel but it is no secret the Israeli president maintains strong contacts with world leaders and often travels abroad to promote peace efforts.
He has headed to Egypt at a time when the Middle East peace process is stumbling forward - but not with any real intent, say the BBC's Christian Fraser in Cairo.
The two men were expected to discuss the fate of Cpl Shalit, who was seized by militants during a raid into Israeli territory in 2006.
The Egyptians, who played a key role earlier this year in establishing the Israeli-Hamas ceasefire in Gaza, are proposing a deal in which Hamas would release the Israeli in exchange for freeing hundreds of Palestinian prisoners.
Separately, it is thought the Israeli president is taking with him to Egypt new ideas for a Middle East peace process.
He is backing a proposal first put forward by Saudi Arabia in 2002 to negotiate a broad peace settlement to include all Arab countries.
The Saudi initiative offers recognition of Israel in exchange for Israel's withdrawal from Arab lands captured in 1967.
Mr Peres has called on Saudi Arabia's King Abdullah to "further" the plan, and despite some opposition at home he has been pushing the idea in meetings with senior Israeli officials.