Witnesses to the attack on Bait Lahya said a barrage of tank fire ripped through several homes early on Wednesday morning.
Medics said a 15-year-old Palestinian, Abd Allah Qahtan, died immediately while two other men, Hamdan Ubaid and his son Hmud, were also killed in the Israeli offensive on civilian homes.
Aljazeera's correspondent reports that Ubaid was an imam of a local mosque and died as he was about to leave home for Fajr (dawn prayers).
"Israeli forces are still opening random fire at these areas ... the situation is absolutely disastrous ... citizens cannot leave their houses even if they are injured or sick," the correspondent added.
A shell also hit a house where families had gathered their children for safety, wounding nine ranging in age from six months to 12 years - several of them seriously - hospital officials said.
Israeli military sources said occupation troops only opened fire after an anti-tank rocket was launched from one of the houses in the town.
"Israeli forces are still opening random fire at these areas ... the situation is absolutely disastrous ... citizens cannot leave their houses even if they are injured or sick"
Hiba Akila, Aljazeera's correspondent in Gaza
Tel Aviv began its campaign - the biggest and bloodiest raid in the Gaza Strip in four years of conflict - after a Hamas rocket strike killed two Israeli toddlers in a border town last Wednesday.
Since the beginning of the intifada in 2000, more than 100 Israeli children have been killed. More than 600 Palestinian children have died in the same period.
The offensive on Bait Lahya is the latest episode in a series of attacks which have killed 88 Palestinians. About 48 of those who died were believed to be part of groups resisting the occupation. Three Israelis have also died.
Meanwhile, Israeli occupation forces shot and killed three Palestinian activists whom they allege belong to the Hamas resistance group.
Guarding the illegal Kfar Darom settlement in southern Gaza, soldiers said they opened fire on three men who showed intent to attack the colony.
One of the three activists died immediately, while the other two initially managed to escape before being hunted down and shot.
A Thai immigrant working in the settlement's greenhouses died after being caught in the exchanges of fire between the three men and the soldiers.
Meanwhile, Israeli tanks and bulldozers have continued to demolish homes in the south of occupied Gaza.
Five homes were levelled in al-Sitar al-Gharbi area after they were deemed too close to the illegal Netzer Hazani settlement.
One of the demolished houses belonged to Ibrahim Hijazi, a top leader of the Popular Front for the Liberation of Palestine.