The rocket fire came shortly after Israel announced it would extend the humanitarian ceasefire for another four hours, as its security cabinet debated whether to press on with the 19-day operation.
The conflict has claimed more than 1,000 Palestinian lives, most of them civilians, and has killed 40 Israeli soldiers as well as three civilians inside Israel.
Top US diplomat John Kerry met European and Middle Eastern foreign ministers in Paris earlier to push both sides to extend the temporary truce, which began at 0500 GMT and was to end at 1700 GMT.
Israel said it had extended the ceasefire for another four hours, but Hamas refused to comment.
Shortly after the original 12-hour window closed, Hamas fired a barrage of rockets at Tel Aviv in central Israel, Ashkelon and Nachal Oz in the south.
Smoke rises from a vehicle, destroyed by an Israeli strike, after Palestinian fire fighters put out the fire, in Gaza City. (AP photo)
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Israel's military said Gaza militants fired projectiles "despite the humanitarian truce being extended", and insisted it would hold fire until midnight local time (2100 GMT).
US Secretary of State Kerry and foreign ministers from Europe and the Middle East earlier urged Israel and the Hamas movement to extend the fragile truce.
"We all call on parties to extend the humanitarian ceasefire," France's Foreign Minister Laurent Fabius told reporters in Paris after meeting Kerry and foreign ministers from Britain, Germany, Italy, Qatar and Turkey, as well as an EU representative.
"We all want to obtain a lasting ceasefire as quickly as possible that addresses both Israeli requirements in terms of security and Palestinian requirements in terms of socio-economic development."
A spokesman for the UN chief said in a statement Ban Ki-moon "urgently appeals once again to all parties to declare a seven-day humanitarian ceasefire in Gaza".
During the 12-hour ceasefire, medics digging through the remains of hundreds of Gaza homes uncovered more than 130 bodies.
The grim discoveries pushed the Palestinian toll in Gaza to more than 1,000 since the conflict erupted on July 8.
Israel also announced the deaths of three more soldiers, raising its military toll to 40, along with two Israeli civilians and a Thai worker killed. On the ground, Palestinian ambulances sped into Gaza neighbourhoods that have been too dangerous to enter for days.
Palestinians ventured onto Gaza's streets after the truce began, some eager to check homes they had fled, others to stock up on supplies.
In many places they found astonishing devastation: buildings levelled, entire blocks of homes completely wiped out by Israeli bombardment.
In northern Beit Hanun, even the hospital was badly damaged by shelling, and AFP correspondents saw the charred body of a paramedic.
There were similar scenes in Shejaiya, where stiff bodies lay on the floor of a room in one building, one caked in dried blood, all of them covered in dust.
Watch video: Israeli military strikes Gaza minutes before 12 hour ceasefire
East of southern Khan Yunis, residents hesitated to enter the Khuzaa neighbourhood, saying Israeli forces remained inside the border area.
And in nearby Bani Suheila, where 20 people were killed in a single Israeli air strike shortly before the truce began, women and children wept as they discovered their homes destroyed.
Hamas and Israel agreed to the "humanitarian window" early on Saturday, after Israel's security cabinet on Friday night rejected a US proposal for a seven-day truce during which the two sides would negotiate a longer-term deal.
Speaking after the rejection, at a news conference in Cairo with UN chief Ban, Kerry said Israel and Hamas "still have some terminology" to agree to on a ceasefire, but added they had "fundamental framework" on a truce.
The two sides remain at odds over the shape of a final agreement to end the fighting, however.
Hamas says any truce must include a guaranteed end to Israel's eight-year blockade of Gaza, while in Israel there are calls for any deal to include the demilitarisation of the Gaza Strip.
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Pro-Palestine demonstrators shout slogans as they wave a Palestinian flag in protest against Israel's military action in Gaza, at Avenue Habib Bourguiba in Tunis. (Reuters photo)
Huge civilian toll
The situation in Gaza has created tensions in the West Bank, where protests against Israel's role in the conflict erupted after Friday prayers and again early Saturday, with a total of eight Palestinians shot dead by Israeli soldiers and settlers.
International concern has mounted over the civilian toll in Gaza.
Rights groups say about 80 percent of the casualties have been civilians, and the UN agency for children UNICEF has said 192 children have been killed during the conflict.
In Tel Aviv on Saturday, thousands of Israelis protested against Israel's campaign against the Palestinian enclave, which it says is aimed at stamping out militant rocket fire and demolishing Hamas tunnels used for cross-border attacks.
"We must not be afraid of peace," said one of the demonstration's organisers.
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Israeli soldiers of the 155mm artillery cannons unit fire towards the Gaza Strip from their position near Israel's border with the coastal Palestinian enclave. (AFP photo)
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