In Israel, the media focused on possible breakthroughs in which the US played no role, highlighting low expectations for Rice's trip.
Foreign Minister Tzipi Livni is increasingly seen as the likely successor to Prime Minister Ehud Olmert.
Corruption allegations by a US businessman have prompted the defense minister to call for him to step down.
The former president arrived in Israel Sunday as Palestinians in Gaza continued to cope with an Israeli-imposed fuel blockade.
Israel agreed Sunday to dismantle 50 West Bank roadblocks after talks with Secretary of State Rice.
Israel refused to reopen crossings or allow crucial fuel supplies into Gaza on Monday, despite UN warnings that vital food aid could be suspended within days.