Palestinian militants fired about 20 rockets over the border after the Israeli ceasefire announcement, and Israel responded with an air attack.
Surrounded by an array of European political leaders, some of whom were highly critical of Israel's tactics in the conflict with Hamas, the Israeli prime minister said his country was not interested in staying in the Gaza Strip.
"We didn't set out to control Gaza, we don't want to remain in Gaza and we intend on leaving Gaza as quickly as possible," he said.
The European leaders had travelled to Israel to lend their support to the ceasefires.
British Prime Minister Gordon Brown said the opening of the crossings into Gaza was important to "make possible a resumption of the talks that are necessary for a permanent peace".
Boasting of victory, Ismail Haniya, the top Hamas leader in Gaza, said Israel had "failed to achieve its goals".
In a speech broadcast on Hamas TV station, he said: "Despite all the wounds, our people didn't surrender, but demonstrated a legendary perseverance."
Hamas said it would hold fire for a week to give Israel time to withdraw its forces from the Gaza Strip.
"Our demand is the withdrawal of the enemy forces from the Gaza Strip within a week, along with the opening of all the crossings for the entry of humanitarian aid, food and other necessities for our people in the Gaza Strip," said Hamas's deputy chief in Syria, Moussa Abou Marzouk.
Meanwhile, the BBC's Paul Wood entered northern Gaza via the Erez crossing as part of the first group of journalists to gain independent access to the Strip from Israel.
Israelis and Palestinians give their views on Israel's ceasefire announcement
He says that in the town of Beit Lahiya he saw the first real destruction - streets churned up by Israeli heavy armour, overturned cars, a lake of raw sewage in the street and a mosque left as a charred ruin.
Hamas officials stopped the BBC from filming at one site where bodies were still being removed - a sign, perhaps, that there had been some kind of military target nearby, our correspondent says.
The BBC's Bethany Bell, on the Israeli side of the border with Gaza, said Israeli helicopters and drones had been flying overhead and Israeli troops were on high alert on Sunday.
Many people are hoping that a ceasefire will last, but no-one on either side of the border will be surprised if the fighting starts up again, she adds.
At least 1,300 Palestinians, according to Palestinian sources, and 13 Israelis have been killed since Israel launched its offensive on 27 December.
Earlier on Sunday, heads of state from across Europe travelled to Egypt for a summit with Egyptian President Hosni Mubarak, Palestinian Authority leader Mahmoud Abbas and UN chief Ban Ki-moon to try to shore up the ceasefire.
Speaking after the talks, UN Secretary-General Ban Ki-moon said he would be sending a team to assess the immediate humanitarian needs of the people in Gaza.
"Within 10 days, I think we'll be able to make an assessment report and we will issue a humanitarian urgent, a humanitarian flash appeal."
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