On Thursday he named George Mitchell as a special envoy, and he has already signaled that the US will reengage the region.
Polls show Benjamin Netanyahu likely to be next prime minister as Israelis vote on Feb. 10.
Hamas may not be able to prevent other factions from attacking Israel, analysts say.
Hamas and Israel have not agreed to terms of a mutual cease-fire agreement, worrying many that the war will soon start up again.
Two key issues are Israel's demand to stop arms smuggling and the Palestinian desire for an end to the economic blockade of Gaza.
Members of the secular Fatah movement, which controls the Palestinian Authority, are divided over how the group should respond to the ongoing Israeli offensive against Hamas.
Palestinian disunity could be a sticking point in cease-fire negotiations.
The Rafah crossing is seen by Israel as a weapons supply line for Hamas and a humanitarian lifeline by Gazans.