Foreign Minister Tzipi Livni is increasingly seen as the likely successor to Prime Minister Ehud Olmert.
The former president said Monday that the Islamist militants are prepared to accept the right of Israel to 'live as a neighbor next door in peace.'
Sixty roadblocks have been removed in the Palestinian territory, but critics say that isn't enough to improve life in the West Bank.
Cairo is working hard for a cease-fire, partly to curb Iran's growing clout.
In the West Bank Tuesday, Secretary Rice urged Israelis and Palestinians to return to the negotiating table.