More than 10 militants from Gaza were shot dead on Monday after infiltrating southern Israel, the army's official spokesman said.
"Hamas terrorists infiltrated Israel through two tunnels from north Gaza. IDF intercepted and killed more than 10 terrorists," Lieutenant Colonel Peter Lerner wrote on his official Twitter feed.
The army said "two terrorist squads" had managed to enter Israel by means of cross-border tunnels, one of which came out just one kilometre (half a mile) from the southern Israeli town of Sderot.
Following an exchange of gunfire with troops, the squad was targeted by an air strike, the army said.
Military radio said the second squad tried to approach Niram kibbutz close to Gaza's northeastern tip, where they engaged in a fierce gun battle with soldiers in which they also fired anti-tank weapons.
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Several soldiers were wounded, the radio said, without giving further details.
A similar attack on Saturday by militants accessing Israel by tunnels from central Gaza left one militant and two soldiers dead, the army said. It said the attackers had been disguised as Israeli soldiers.
Monday's attack was claimed by Hamas armed wing the Ezzedine al-Qassam Brigades, which said it had carried out "an operation behind enemy lines in response to the massacre in Shejaiya."
It was referring to a neighbourhood between Gaza City and the Israeli border, where a ferocious Israeli bombardment, which began early on Sunday, has killed at least 72 Palestinians.
Late on Thursday, Israel sent ground troops into Gaza on a mission to destroy a network of sophisticated tunnels used by militants for launching cross-border attacks.
"Since the beginning of the ground phase of the operation, the IDF has exposed 14 tunnels headed towards Israel, all intended to infiltrate Israel and carry out terror attacks," Lerner said in a statement late on Sunday.
"It's like the 'Underground', the 'Metro' or the 'Subway'. These tunnels are all connected. I would describe it as 'Lower Gaza'," he said.