Ahmed Aboul Gheit, the Egyptian foreign minister, said: "The necessary thinking which everyone must focus on ... is on how to conceptualise what is referred to as the endgame. The endgame is the Palestinian state.
"If we agree on a Palestinian state, its borders and its parameters, then we can deal from there, through negotiations, to try and achieve this aim."
The Egyptian idea is similar to a concept outlined by King Abdullah of Jordan in a recent interview in Time magazine.
Hosni Mubarak, the Egyptian president, flew to Jordan on Sunday to discuss the plan with King Abdullah.
Most previous attempts to reach agreement between the Israelis and Palestinians have been based on building confidence through a series of small steps.
The 2003 "road map" document leaves the details of the Palestinian state to be decided during Israeli-Palestinian negotiations, and has not yet produced any significant progress towards peace in the region.
In Time magazine, King Abdullah said: "We want to jump ahead to something tangible. We need to get to the point where people want to sign on the dotted line. We want to move to a two-state solution, but we are not going to go back and forth with lawyers until we get there."
After the brief talks in Amman, Egypt and Jordan stressed the need to work for a speedy resumption of Middle East peace talks, officials said.
The two leaders agreed that an end to the Arab-Israeli conflict was only possible through a comprehensive settlement based on past UN resolutions and a land for peace deal.
The European Union has also promised to work harder for peace in the region after the conflict in Lebanon.
"We want to move to a two-state solution, but we are not going to go back and forth with lawyers until we get there."
King Abdullah of Jordan
Javier Solana, the EU foreign policy chief, said that the EU should persuade the United States to update and relaunch the "road map" and should seek talks based on a return to Israel's 1967 borders except for land that the opposing sides had agreed to swap.
Israel is unlikely to agree to return to its 1967 borders and has said it wants to keep major settlement blocks in the occupied West Bank.
A Palestinian teenager has been killed and his brother critically wounded during exchanges of fire between Israeli forces and Palestinians outside Rafah in southern Gaza, Palestinian sources said.
An Israeli army spokesman told the AFP news agency that "our forces identified several people moving in a suspicious manner, who were thought to be planting explosive devices, opened fire and hit them".
The army started the incursion into southern Gaza on Wednesday as part of a major offensive it began after a soldier was seized by Palestinian gunmen in a cross-border raid on June 25.