The IDF told YNetNews that it thwarted the Hamas militant plan to kidnap an IDF soldier during the attack, which fell on Israel's 59th Independence Day.
A spokesman for the Hamas group said the attacks were in retaliation for recent Israeli military actions in which nine Palestinians, most said to be militants, were killed.
"The party that ended the calm is the Israeli occupation, which has never been committed to the conditions of the mutual calm," Fawzi Barhoum, a Hamas spokesman said, apparently referring to a 5-month-old cease-fire in Gaza, the Financial Times reported. "We are responding to defend our people and resistance is continuing."
Israeli Prime Minister Ehud Olmert met with military advisers to determine an additional response to the attack, YNetNews said.
The Hamas-led Palestinian government issued a statement after the attack calling on both sides to resume the cease-fire.
"The government reiterates its desire that the calm continue and be preserved in the way that achieves the national interests of the Palestinian people," government spokesman Ghazi Hamad said, YNetNews reported.