Local media cited Palestinian health officials as saying that the attack killed one Palestinian and wounded another three, including two passers-by.
The spokeswoman said the militants had launched two shells into Israel, dealing another blow to a fragile truce declared two weeks ago. The ceasefire followed a three-week Israeli offensive which saw some 1,300 Palestinians, mostly civilians, killed and more that 5,300 injured and caused widespread damage and destruction.
According to the Israeli military, Palestinian militant groups have launched some 30 rockets and shells during the two weeks since the end of Israel's operation in Gaza.
"If there is shooting at residents of the south, there will be an Israeli response that will be harsh and disproportionate," Prime Minister Ehud Olmert said at a government meeting on Sunday.
Egypt is mediating talks between Gaza-ruling Hamas and Israel on a long-term truce. Hamas demands that Israel lift its blockade of Gaza as a condition for the truce.
