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Three mortar shells fired from Gaza hit southern Israel on Thursday, the army said, just over two hours after a humanitarian ceasefire took effect.
The shells struck in the region of Eshkol, which borders the southern Gaza Strip, the army told AFP, blaming Hamas but without giving further details.
There were no immediate reports of any damage or casualties.
Hamas denied any involvement in the attack.
"Whenever the Palestinian factions say that we are not going to do anything, they don't," said Ihab Ghussein, the media office chief for the former Hamas government in Gaza.
The truce "was violated by the Israelis, as usual," he added, saying Israeli tanks had fired several shells into southern Gaza during the ceasefire.
The Israeli army later said an explosion near the border wounded one soldier, without giving any details of the location of the blast.
The military responded with artillery fire.
The attacks interrupted a ceasefire called for by the UN on humanitarian grounds, which both Israel and Hamas had agreed to observe between 0700 GMT and 1200 GMT.
Fighting since Israel launched Operation Protective Shield on July 8 to stamp out rocket fire by Gaza militants has killed 231 Palestinians, many of them women and children, and one Israeli.
Israel has carried out more than 1,750 attacks in Gaza, mostly air strikes, the army says, and militants have fired nearly 1,400 rockets, 1,048 of which have hit the Jewish state.