Israel, which occupied the Gaza Strip in 1967, pulled troops and settlers out in 2005 but still controls its northern and eastern borders, airspace and coastal waters, and has imposed a blockade it says is meant to counter militant rocket fire.
Deputy Defense Minister Matan Vilnai said Israel wanted to wash its hands of Gaza altogether by handing over the supply of electricity, water and medicine to others. An Israeli security official said Egypt should take over responsibility.
"We need to understand that when Gaza is open to the other side, we lose responsibility for it. So we want to disconnect from it," Vilnai said.
Hundreds of Gazans on Thursday streamed past the flattened border wall into Egypt on foot or donkeys to stock up on goods in short supply, including sheep, motorcycles and medicines.
A spokesman for Hamas, which violently took control of Gaza after routing Palestinian President Mahmoud Abbas' Fatah forces in June, rejected Vilnai's idea as an attempt to separate Gaza from the occupied West Bank.
According to the official WAFA Palestinian news agency, Abbas also said Israel might seize the chance to sever Gaza from the West Bank, the other territory he wants for a state, and warned of "grave consequences" for a U.S.-backed peace drive.
Egypt declined comment on Vilnai's proposal. When asked what Cairo planned to do, Egyptian Foreign Ministry spokesman Hossam Zaki said the situation was "temporary" and that "every option is under consideration."
Militants set off bombs Wednesday destroying Gaza's southern border wall in the town of Rafah, where Egyptian forces are posted, allowing tens of thousands of Palestinians to pour through to stock up on goods in short supply.
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