Hamas emergency services spokesman Adham Abu Selmiya named the victim as 17-year-old Amjad al-Zaanein, saying he died after being hit by Israeli tank fire near the northern town of Jabaliya.
One of the two wounded men, who were hit by shrapnel, was said to be in critical condition, he added.
The casualties occurred as Israeli troops mounted an incursion into the northern Gaza Strip, witnesses and members of the Hamas-run security forces said.
The tanks, which pushed about 400 metres (yards) into the coastal enclave at around 9:00 am (0700 GMT), were accompanied by a bulldozer and were still there by mid-afternoon, they said.
The Israeli army said the incident began when Palestinians detonated an explosive device targetting an army patrol along the border without causing casualties.
"A short while after the incident, soldiers identified two militants handling the device trigger system and consequently opened fire on them. A hit was confirmed," a military spokeswoman told AFP.
She could not immediately confirm if Israeli forces had crossed the border.
Israel has often demolished structures and cleared land along Gaza`s border with the Jewish state, citing security concerns.
Israel and Hamas are formally committed to a truce agreed after Israel`s devastating 22-day Operation Cast Lead, which ended exactly two years ago on January 18, 2009.
But in recent months, militants have fired dozens of rockets into southern Israel, prompting retaliatory Israeli airstrikes.
Last week, following rising tensions along the border, Hamas said it would ensure militants groups kept to the truce agreement.
However, on Monday, militants fired a Qassam rocket into southern Israel, followed by four mortar shells on Tuesday morning, the army said.
The Popular Resistance Committees, a coalition of militant groups, claimed responsibility for the mortar fire. (*)
Editor: Kunto Wibisono
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