The agreement may mark a break with a longstanding Israeli and American boycott of the Islamic militant organization, giving Hamas incentive to enforce the deal.
The temporary cease-fire deal bids to end attacks from Gaza militants and the Israeli army and improve life in the impoverished coastal strip.
In Israel, the media focused on possible breakthroughs in which the US played no role, highlighting low expectations for Rice's trip.
The Islamist militant group has controlled the coastal strip for a year now and says it will not relent to international pressure.
Three Fulbright scholars are waiting to see if Israel will allow them to leave Gaza to study in the United States.