It was not immediately clear whether the minister, Matan Vilnai, was expressing the view of the Israeli government, or was testing international receptiveness to such idea.
Privately, several Israeli officials have said Wednesday's breach of the Gaza-Egypt border by Palestinian militants was a positive development that would ease pressure on Israel to keep providing for Gaza's basic needs, and could pave the way for increasingly disconnecting from the territory.
Egypt in the past has resisted a link with Gaza, and it was uncertain how it would react to such an idea, though a top Egyptian official said Thursday that Egypt's border with Gaza will go back to normal, and strongly rejected Israel's plan to sever ties.
"This is a wrong assumption," Hossam Zaki, the official spokesman for Egypt's foreign ministry, said of Israeli hints that it was thinking of giving up all responsibility for Gaza, including supplying electricity, now that the territory's southern border with Egypt is open.
"The current situation is only an exception and for temporary reasons," Zaki said. "The border will go back to normal."
On the Gaza-Egypt border, Egyptian border guards began trying to control the masses of Palestinians flooding across the border for a second day Thursday, stopping some from moving deeper into Egypt, but not attempting to reseal the border.
Before Wednesday, gunmen had blown down the border wall, and tens of thousands of Gazans, cooped up by border closures for two years, had rushed into Egypt. The breach effectively ended Israel's tight blockade of Gaza, imposed last week in response to a spike in rocket attacks on Israeli border towns.
In the past two days, Gazans have stocked up on supplies in Egypt, including cement, fuel, cigarettes and other staples. In response, Israel stopped emergency shipments of industrial diesel fuel, arguing that Gazans were now able to get supplies from Egypt. However, Palestinian officials said Gaza's power plant would shut down Sunday, for a second time in a week, if the fuel shipments don't resume.
Israel is worried that along with the fuel, cigarettes and medicine moving back into Gaza through the chaos, some Gazans may smuggle in guns and explosives, reports CBS News correspondent Richard Roth.
Vilnai suggested Thursday that Israel views the border breach as an opportunity to disconnect from Gaza. Israel withdrew from Gaza in 2005, after a 38-year military occupation. However, the international community has not accepted Israel's contention that its occupation - and with that Israel's responsibility for Gaza's civilians - ended entirely with the pullout since Israel still controls most access to Gaza.
Vilnai said Thursday, in comments confirmed by his office, that "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," he was quoted as saying. "We want to stop supplying electricity to them, stop supplying them with water and medicine, so that it would come from another place."
Israel will continue to be responsible for the flow of such supplies into the Gaza Strip until an alternative is found, the office quoted him as saying.
Gazans, meanwhile, hoped that the temporary border opening will become permanent. Both Egypt and Israel had restricted the movement of people and goods in and out of Gaza after Hamas won parliament elections in 2006, and further tightened the closure after Hamas seized control of the area by force.
"The Egyptians started doing good deeds by letting us in. For God's sake, why don't they keep allowing us to pass through?" said Mohammed Abu Amra, a Palestinian walking across the border on crutches. "Everyone is rushing into Egypt before they seal it off."
The border breach has boosted the popularity of Gaza's Hamas rulers, who in recent months had struggled to rule because of border closures. The sanctions have led to severe shortages of cement, cigarette and other basic goods, deepened poverty and drove up unemployment.
Hamas has used the border breach - carefully planned, with militants weakening the metal wall with blow torches about a month ago - to push its demand for reopening the border passages, this time with Hamas involvement. Such an arrangement would in effect end the international sanctions against the Islamic militants.
Hamas government spokesman Taher Nunu suggested Thursday that Hamas would seek a role in a future on the Gaza-Egypt border. "An open border like this has no logic," he said. "We are studying the mechanism of having an official crossing point."
However, it's not clear whether Egypt will acquiesce. Egyptian President Hosni Mubarak has been under intense public pressure at home in recent days to alleviate the suffering of Gazans under blockade. However, Egypt would likely be reluctant to have an open border with a territory ruled by Islamic militants.
In other developments:
An Arab diplomat said Egypt told the U.S. it expects the Palestinians' exodus from Gaza to end by midday Thursday, but a senior U.S. official said Egypt has not been precise about when it will stop the flow.
In Tel Aviv, visiting US Undersecretary of State Nicholas Burns said that while Hamas itself was to blame for the shortages in the Gaza Strip, it was for Egypt to restore order at the frontier.
"Obviously it is going to be up to the Egyptian government to bring under control the situation along the border," he said at the start of a meeting with Israeli Cabinet minister Shaul Mofaz.
Egyptian border guards were patrolling access roads to the border Thursday. Police in helmets and with sniffer dogs used batons to beat the hoods of private cars and pickup trucks that massed at the border to carry Palestinians further into Egyptian territory.
Cargo shipments across the border picked up Thursday, using the back-to-back system. Trucks and donkey carts pulled up to the Egyptian side, the goods were unloaded and carried across to the Gazan side were they were put in waiting trucks.
Gaza businessman Abu Omar Shurafa received a shipment of 100 tons of cement, seizing an opportunity to stock up before the border closes again. "Everyone is exerting all efforts to stock the reserves for six to seven months. We have to find a way to continue living," he said.
Still, he was also hopeful that this could be the beginning of a new arrangement. "A solution has to be like this," he said, referring to the flow of goods from Egypt.
Some Gazans just wanted to get out, even for a few hours.
"We just want freedom," said Adel Tildani, who was bringing his mother-in-law from Egypt into Gaza to meet grandchildren she had never seen before. "I don't need to buy anything. Freedom is more important."