On Thursday in Egypt, Israeli President Shimon Peres backed the 'spirit' of a Saudi proposal that offers Arab recognition of Israel.
The outgoing Israeli Prime Minister Ehud Olmert said Israel may have to withdraw from the West Bank if it wants peace with Palestinians, making Tzipi Livni's job of building a new government coalition with hard-liners much more difficult.
Forming a single binational state is among the alternatives being raised to the two-state solution.
Networks of tunnels underneath the Egypt-Gaza border are used to ferry everything from food to weapons into the impoverished Gaza Strip.
Ms. Rice concludes a one-day trip to the region Monday. Her 22 visits have netted little progress.