"Israeli ground forces opened fire Wednesday morning on terrorists operating near Khan Younis, around the security barrier," he said.
The incident occurred close to where Palestinian fighters fired 30 rockets into Israel on Tuesday, the Israeli military said.
Israeli troops killed three Palestinian Hamas fighters in Gaza City and wounded five more people in response to the rocket attacks.
In a separate development on Wednesday, Israel's security cabinet said the country's army has been told to prepare for possible military action if mediation efforts backed by Egypt to reach a truce in the Hamas-controlled Gaza Strip fail.
"The Security Cabinet decided this morning to support Egyptian efforts to achieve calm in the south and to end the daily targeting of Israeli civilians by the terrorists in Gaza," Mark Regev, a spokesman for Ehud Olmert, Israel's prime minister, said.
"In parallel, the security cabinet has instructed the military to continue its preparations in the unfortunate event that the Egyptian track should prove unsuccessful."
David Chater, Al Jazeera's correspondent in Jerusalem, said that Israel is "preparing for a heavy military incursion into the Gaza Strip".
"Many ministers are saying ... that it's important that Israel should launch a heavy punch against Hamas before any truce is concluded," he said.
"The security cabinet met for about four hours ... the decision is, apparently, that the Israeli's will continue to explore the options created by the Cairo initiative for the six month Gaza truce.
"So one hand is being held out towards peace, towards the idea of a truce, while the other one is a bunched up fist ready to hit Hamas and the Gaza Strip hard."
Gaza territory is effectively controlled by Hamas since its forces routed fighters loyal to Fatah, its main rival, in June 2007.
Israel pulled out of Gaza in 2005 but still maintains a harsh blockade on the territory.
It has in the past restricted fuel deliveries to Gaza, resulting in widespread and protracted power cuts.