Gaza City and Israel's Eshkol hit by deadly blasts
Gaza and southern Israel have seen an upsurge in violence despite a plea by the UN secretary general for a cessation of hostilities.
Explosions in Gaza City reportedly killed 10 people, including children.
Israel confirmed five of its soldiers died on Monday - one inside Gaza and four in a mortar attack along the border. Five Hamas militants were also killed inside Israel, officials said.
Israeli PM Benjamin Netanyahu warned of a "prolonged" Israeli campaign in Gaza.
"We will continue to act aggressively and responsibly until the mission is completed to protect our citizens, soldiers and children," Mr Netanyahu said.
Calling Monday a "painful day", Mr Netanyahu said Israel would not finish its operation until it had "neutralised" Hamas tunnels out of Gaza.
Fighting between Israel and Hamas has claimed more than 1,030 Palestinian lives, most of them civilian, since 8 July, when Israel launched an offensive against Hamas in Gaza after a surge in rocket fire.
On 18 July, it extended operations with a ground offensive, saying it was necessary to destroy tunnels dug by militants to infiltrate Israel.
Israel's military death toll rose to 48 with Monday's deaths. Three civilians have also died.
Early on Tuesday, the house of Hamas leader Ismail Haniyeh was hit by an Israeli air strike, according to his son, but no casualties were reported.
Earlier, UN Secretary General Ban Ki-moon urged an immediate halt to the violence in Gaza, saying the Palestinian territory was in a "critical condition".
Mr Ban, who spoke in New York after returning from a visit to the region, was critical of both sides for firing into civilian areas.
He said Hamas had fired missiles into civilian areas of Israel, while Israeli forces had used high-explosive weapons in the crowded Gaza Strip.
The secretary general repeated the UN's call for an immediate, unconditional humanitarian ceasefire in Gaza during the Muslim Eid al-Fitr holiday.
Later, the French presidency said the leaders of the United States, France, Germany, Italy and Britain - who held telephone talks - had "agreed to redouble their efforts to obtain a ceasefire. Pressure must increase to get there".
At least 10 people - eight of them children - were killed in Monday afternoon's blasts in Gaza City, Palestinian health officials said.
Palestinian officials say the 10 were killed by Israeli missile strikes, but Israel says the explosions were caused by rockets misfired by "terrorists".
Four Israeli soldiers were killed and another 10 injured when a mortar shell hit the Eshkol district.
The Israeli military said the five Hamas militants who died had entered Israel via a tunnel from Gaza and opened fire on Israeli troops, who returned fire.
At the scene: Martin Patience, BBC News, Gaza City
There was chaos, confusion, and grief as the latest casualties of this conflict were rushed into Gaza's main hospital.
Among the victims were children, caught up in a conflict they cannot possibly understand. They had been playing outside during a lull in the fighting.
One man told me he was at home when he heard a huge explosion. He rushed outside and the street was full of bodies.
Hamas says the children were hit by an Israeli strike. But Israel denies this - saying the blast was caused by a misfired Palestinian rocket.
The attack punctured what had been a day of relative calm in Gaza.
Today was the start of a three-day religious festival to mark the end of Ramadan. Some Gazans prayed in mosques damaged by the fighting. You could see children playing in the park on swings.
Eid al-Fitr is supposed to be a time of joy and celebration. But for the moment there is only sorrow and anger in Gaza.
At the scene: Bethany Bell, BBC News, Jerusalem
While Israel's PM Benjamin Netanyahu is facing increasing international pressure for a ceasefire, at home there is strong public support for the offensive in Gaza.
A poll published by Israel's Channel 10 TV on Sunday suggested 87% of Israelis were in favour - and just 7% wanted a full ceasefire.
There are concerns about the rising number of casualties among Israeli soldiers but people here want the rocket fire on Israel to stop. The sound of sirens over central and southern Israel has become part of everyday life. And many are very concerned about the new threat posed by the network of cross-border tunnels from Gaza.
At her home on a kibbutz close to the Gaza border, one woman said she was afraid. Rockets can be intercepted by Iron Dome, she told me, referring to Israel's missile defence system.
"But there's no Iron Dome protection against Hamas fighters coming up through the tunnels to kidnap and kill us."
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