Israel and the US don't want rebuilding homes to become rebuilding Hamas.
Polls show Benjamin Netanyahu likely to be next prime minister as Israelis vote on Feb. 10.
On Thursday in Egypt, Israeli President Shimon Peres backed the 'spirit' of a Saudi proposal that offers Arab recognition of Israel.
Ms. Rice concludes a one-day trip to the region Monday. Her 22 visits have netted little progress.
Hamas says that Gilad Shalit could be released in a week, but terms of a deal with Israel keep shifting.