Israel said it was not sure how long the diplomatic process would take and that a working arms embargo on Hamas was needed.
BBC world affairs correspondent Paul Reynolds says Israel has always said that it will accept an outcome under which rockets and smuggling are stopped - but there is a potentially long gap between accepting principles and applying practice.
Security sources have confirmed senior Israeli defence official Amos Gilad will travel to Cairo on Thursday to discuss ceasefire options.
Rice: The US supports the Franco-Egyptian initiative
Palestinian Authority leader Mahmoud Abbas is expected in Cairo a day later for talks.
In a statement on Wednesday, France's President Nicolas Sarkozy welcomed "the acceptance by Israel and the Palestinian Authority" of the Franco-Egyptian ceasefire plan. The statement did not mention Hamas.
Tony Blair, Middle East envoy for the Quartet of the UN, US, Russia and EU, told the BBC he was hopeful that the ceasefire proposal would succeed.
The building blocks of a plan had been agreed but the details had still to be worked out, he said, which would take hard work over the coming days.
The BBC's Jeremy Bowen on the Israel-Gaza boundary says the end may not be in sight yet, but there are now indications of what the two sides want from a ceasefire.
A compromise on securing Egypt's border with Gaza, stopping the movement of weapons, and on opening border crossings between Israel and Gaza could give both Israel and Hamas something tangible, our correspondent says.
But the problem from Israel's point of view is that Hamas would then be able to say that Palestinian resistance had forced Israel to lift the siege of Gaza, our correspondent adds, which is precisely what Israel - which seeks a severely weakened Hamas - does not want.
The diplomatic developments came as Israel halted military operations in Gaza for three hours to create "humanitarian corridors" for supplies and fuel, the first of what an Israeli spokesman said would be a daily ceasefire.
News agencies reported that Gaza residents had rushed out into the streets during the lull to stock up on food and visit relatives in hospital.
A Hamas spokesman said that the group would not launch any missiles at Israeli targets during the lull.
The respite was brief, however. The Israeli army says it attacked dozens of targets throughout the day and that more than 20 rockets were fired into Israel from Gaza.
Israel has been criticised by aid agencies who have warned of a mounting humanitarian crisis for the 1.5 million Palestinians in Gaza, who are unable to escape from the conflict because of Israel's blockade.
Christopher Gunness, a spokesman for the UN relief agency Unrwa, said the move did not go far enough.
"When you are trying to feed 750,000 people a day in Gaza as we are, you need a permanent ceasefire. You can't do that in a three-hour window," he said.
The World Bank also warned on Wednesday of a looming public health crisis in Gaza because of damage to its sewage system and a shortage of clean drinking water.
Israel's decision to facilitate "humanitarian corridors" followed one of the deadliest days since the offensive began last month, with more than 130 people killed on Tuesday.
Shopping for 'basic needs' in Gaza market
Since the start of its military operation in Gaza, Israel has lost seven soldiers on the ground.
Militants have also launched hundreds of rockets into Israel, killing four people.
Casualty claims in Gaza cannot be independently verified.
Up to now, the BBC has had Palestinian producers reporting from Gaza but international journalists have not been allowed in.
On Wednesday, Andrew Herbert, a BBC video journalist, went in on a patrol with the Israeli army.
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