Israeli and Palestinian officials met in Cairo Sunday in a bid to bolster the current cease-fire.
Israel and the US don't want rebuilding homes to become rebuilding Hamas.
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.
Israel seeks US help on Gaza weapons smuggling, while Arab nations remain divided over a truce.
Sari Bashi of the group Gisha argued before the Israeli Supreme Court Thursday that Israel is still responsible for Gazan civilians because it controls the enclave's borders, airspace, and sea space.
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.