Hamas says that Gilad Shalit could be released in a week, but terms of a deal with Israel keep shifting.
Israel to release up to 150 Palestinian prisoners later this month.
The Palestinian factions fought Saturday in the worst internal violence since Hamas's Gaza coup.
Hamas arrested senior Fatah officials in Gaza on Friday, capping off one of the worst weeks of conflict between the two Palestinian factions.
Israeli prime minister resigns from his post, but vows to pursue a deal with Palestinians and Syrians.
Explosions and a Hamas-led crackdown on the rival Fatah Party has raised tensions to their highest levels since Hamas seized control of the Palestinian territory in 2007.
The latest stops in his Mideast tour included the rocket-besieged Israeli town of Sderot and the West Bank town of Ramallah.
Obama likely to return US to role of 'honest broker.' McCain sees fighting Islamic extremists as paramount.