The three men -- all members of the hardline Islamic Jihad faction – were killed by tank fire near the village of Qarara, a Palestinian medic said.
Troops identified "hitting" three Palestinians who were "carrying large bags and acting in a suspicious manner" as they approached the security fence that separates Israel from Gaza near Kissufim, an army spokesman said.
Further north, five Palestinians were wounded and another five detained after Israeli tanks and troops moved across the border into a territory the military had abandoned last September after a 38-year presence.
At least 184 Palestinians and one Israeli soldier have died in Gaza since Israel launched its offensive on June 28, but the violence has been largely overshadowed by the deadlier conflict in Lebanon.
The Summer Rain operation was triggered when Gaza militants, including members of the armed wing of the governing Hamas movement, killed two soldiers and seized a conscript corporal in a cross-border raid on June 25.
Five people were detained in the latest incursion, including at least two affiliated to Hamas, before troops withdrew from the area.
"IDF (Israel Defence Force) soldiers surrounded a house in which five wanted terrorists were located. After exchanges of fire, one Hamas gunmen was hit and all the wanted Palestinians were taken for investigation," a spokesman said.
Three of the five wounded belonged to Hamas's Ezzedine al-Qassam Brigades military wing, Palestinian sources said.
An Israeli soldier was also lightly injured by shrapnel from an anti-tank missile and treated at the scene, the army said.
Wedged into tanks and armoured vehicles, soldiers moved up to 600 metres into Palestinian territory between the Karni and Nahal Oz crossings that separate Israel from Gaza, security sources and witnesses said.
Troops were bulldozing land and shooting could be heard, the sources said, in an operation that came after two overnight Israeli air strikes.
Forces also crossed into southern Gaza where on Tuesday they were looking for tunnels dug by militants, an army spokesman said.
Israel has also pressed a West Bank crackdown on Hamas, detaining more than 60 elected officials, including a third of the cabinet and more than two dozen MPs.
An Israeli military court charged parliament speaker Aziz Dweik on Tuesday with "belonging to a terrorist organisation" 17 days after his arrest.
In a telephone call to Palestinian MPs, Jordan's parliament speaker Abdel Hadi al-Majali expressed solidarity with lawmakers who have been arrested and urged "all peace-loving forces" in the world to immediately seek their release.
Calls to release journalists
Palestinian prime minister Ismail Haniya, head of the Hamas-led government, renewed calls for the release of two Western journalists working for US television network Fox News who were kidnapped eight days ago.
"I asked the interior minister (Said Siam) to act as quickly as possible in order to retrieve the two men and arrest their abductors," he said.
There has been no news of the whereabouts of US reporter Steve Centanni and freelance cameraman Olaf Wiig from New Zealand, snatched in Gaza City in the latest in a string of kidnappings in the lawless territory over the past year.
Living conditions for the 1.4 million people in Gaza have sharply deteriorated since Israel bombed its only power station in June and the West suspended direct aid to the Hamas-led government in March.