A Qassam rocket struck an open area in Sha'ar Hanegev Monday evening, despite separate cease-fire declarations by both Israel and Hamas which ended Israel's three-week military offensive in the Gaza Strip last month.
The rocket caused no injuries or damage.
Earlier Monday, three mortar shells hit the Eshkol region, also causing no injuries or damage.
In response to the mortar attack, the Israel Air Force bombed a car in the southern Gaza Strip. Palestinian medical workers reported that one person had been killed in the bombing, and three others were wounded.
The Israel Defense Forces said it targeted gunmen who had fired the mortars.
Witnesses said the air-strike hit the men while they were traveling in a car in the town. Their identities were not immediately known.
Late Sunday, IAF aircraft bombed a Hamas security building in the central Gaza Strip and two other targets in the southern coastal territory, Palestinian witnesses said, also in response to a spate of cross-border rocket fire.
Witnesses in the central Gaza village of Mughraqa said a missile struck after dark in a cluster of caravans that served as a Hamas security headquarters.
They said the site had been evacuated, apparently after Israel telephoned warnings to Palestinians in Gaza to leave any buildings where weapons were located.
The other two strikes were on suspected sites of tunnels along the border with Egypt, Hamas said. Palestinians reported huge explosions as Israeli warplanes dropped bombs on the border, where Hamas operates tunnels to smuggle in weapons, food and other goods.
Before the attack, Israeli aircraft flew over the Gaza-Egypt border, setting off sonic booms, and witnesses said hundreds of people who work in the tunnels there fled, along with residents.
The news comes as Israel's leadership warned Sunday that the response to the rocket attacks from Gaza would be fierce. The disagreements between Prime Minister Ehud Olmert and Foreign Minister Tzipi Livni, on the one hand, and Defense Minister Ehud Barak over an "arrangement" with Hamas have intensified.
On Sunday Israel suffered the heaviest barrage of rocket and mortar attacks since a unilateral cease-fire went into effect more than two weeks ago.
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