And Hamas's de facto rule of the strip since June, following infighting with rival Fatah, has only stoked calls in the Jewish state for a big military sweep.
Late on Tuesday, Israeli aircraft bombed a police station in southern Gaza, killing at least four Hamas policemen, hospital officials said.
The Israeli military confirmed its forces carried out the shelling in Abasan village, near the city of Khan Younis. An earlier air attack on the Jabalya refugee camp wounded six civilians, according to hospital sources.
Speaking to reporters earlier, Ehud Barak, Israel's defence minister, said: "Every passing day brings us closer to a broad operation in Gaza.
We are not looking forward to it [and] we would be happy if circumstances prevented it."
'Collective punishment'
Israel, which controls official Gazan border crossings, began reducing the amount of fuel pumped to Gaza this week. It also wants to reduce power supplies, but has put that on hold.
The sanctions, which were put together by Barak, prompted UN and EU delegates to urge Israel not to impose "collective punishment", illegal under international law, on Gaza's 1.5 million residents.
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"The question is will Fatah be strong enough to contain such a powerful 'partner' or will it be just exploited and eroded over time?
Werewolf, Micronesia
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Israel's attorney-general also opposes cutting electricity supplies to Gaza on humanitarian grounds.
Britain said on Tuesday it was "deeply concerned" by reports that Israel had reduced Gaza's fuel supply and was considering electricity cuts, and had spoken to the Israeli government about the matter.
Makeshift Palestinian rockets have killed two Israelis this year.
Hamas has not claimed recent attacks, but Israel's military says Hamas is carrying out an arms build-up that will make it a serious fighting force.
Weighed against an invasion of Gaza is a US-organised peace conference in November between Ehud Olmert, the Israeli prime minister, and Mahmoud Abbas, the Palestinian president, who affectively only rules the occupied West Bank.
While Olmert may want calm, he is also under pressure from right-wing coalition partners to hit Hamas hard.
Haim Ramon, Israel's vice prime minister, when asked about a possible Gaza invasion, said: "The present situation will not last."
"I prefer that we use sanctions. I believe that the implementation of sanctions will be effective. But we have our doubts about it."
In the interview with Reuters news agency, he added: "If they stop sending rockets over, our need for the weapons of sanctions, or other weapons, will not be an issue."