Hosni Mubarak, Egypt's president, called to congratulate Ehud Olmert on his being asked by the Israeli president on Thursday to head a government after winning the general election last month.
A statement from the Israeli prime minister's office said: "The two agreed to meet immediately after a government is formed."
Mubarak also wished Olmert good luck at forging a coalition.
Egypt, the first Arab country to sign a peace treaty with Israel, in 1979, has long been active as a mediator in the Israeli-Palestinian conflict.
Mubarak played an important role in achieving a ceasefire deal last year between Israel and Palestinian resistance groups.
Olmert said earlier on Thursday that he hoped to put together a government as quickly as possible, although such political bargaining traditionally takes weeks in Israel.
Ehud Olmert (R) wants to set
His centrist Kadima party has said it would formally launch coalition talks with several political parties on Sunday.
Olmert won the election on March 28 on a platform to set Israel's borders with the Palestinians, with or without their agreement, within four years.
He plans to do this by keeping several large settler blocs within a separation barrier Israel is building in the West Bank, and dismantling smaller enclaves outside it.
Palestinians object to Israel's plan, saying it would deny them a viable state in the land Israel captured in the 1967 Middle East war.