Israeli Prime Minister Benjamin Netanyahu vowed that Israel would use "all necessary means" to protect its citizens following the attack and the head of the opposition called for a repetition of a bloody 2008 Israeli incursion into the coastal strip.

Hours after the main exchange, the Israeli military said troops shot two men seen moving suspiciously toward a frontier "no-go" zone in the north of the coastal enclave.

"An army force spotted two suspects moving toward the border fence and opened fire," a spokeswoman said. "The two were seen to have been hit."

Palestinian officials said Israeli tanks fired several shells into Gaza after dark but they had no reports of casualties.

The armed wing of Gaza's ruling Hamas movement took responsibility for the mortar barrage, three days after an Israeli air strike killed two of its members in Gaza.

AFP