An upsurge in violence has been seen in Gaza and southern Israel despite a plea by UN Secretary General Ban Ki-moon 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,” Benjamin Netanyahu said.
Calling Monday a “painful day”, Benjamin Netanyahu said Israel would not finish its operation until it had “neutralized” 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 July 18, 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.
Earlier, Ban Ki-moon urged an immediate halt to the violence in Gaza, saying the Palestinian territory was in a “critical condition”.
Ban Ki-moon, 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 US, 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.
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