Three other people were injured in the incident late on Tuesday, which involved an Israeli air strike.
Israeli border troops and Hamas fighters fired at each other after the soldiers moved to destroy "a tunnel aimed at abducting soldiers" about 300m inside Gaza.
'Enemy will pay'
During the clashes, Dr Moaiya Hassanain, a Palestinian health ministry official, said one Palestinian - Mazen Seada, a senior Hamas commander in central Gaza - was killed and three were wounded, including a woman.
Shortly afterwards, Hamas said it fired mortars at southern Israel and the army said it launched an air strike at the mortar launchers and hit them.
Hamas radio confirmed that four fighters were killed in the air strike.
"The aggression is a major violation of the agreement. If such raids are repeated, fighting will not be limited only to the area east of the central Gaza Strip"
Sami Abu Zuhri,
Gaza medics said another fighter was killed by a tank shell.
Hamas vowed revenge, saying on its military wing's website that its "response will be harsh, and the enemy will pay a heavy price".
Sami Abu Zuhri, a Hamas spokesman, said the raid proved that Israel was not interested in continuing the ceasefire although he stopped short of saying that Hamas would abandon it.
"The aggression is a major violation of the agreement. If such raids are repeated, fighting will not be limited only to the area east of the central Gaza Strip," Abu Zuhri said.
A senior Israeli military official speaking on condition of anonymity said the tunnel had been dug from inside a Gaza home, illustrating that Hamas was using civilians for cover.
Both sides claimed they had not violated the Egyptian-mediated truce reached in June after months of indirect negotiations that halted a deadly cycle of Palestinian rocket attacks and Israeli bombardment.
The army said it was acting to remove an immediate threat to Israel while Hamas said it was trying to prevent an Israeli incursion.
Despite the truce, Israel has closed its crossings into the coastal strip of 1.4 million Palestinians and mostly kept the crippling siege it imposed on the area after Hamas forcibly took over the territory from Fatah forces loyal to Mahmoud Abbas, the Palestinian president, in June last year.
Sporadic rocket attacks on southern Israel from Gaza have also persisted in spite of the ceasefire.
Gilad Shalit, an Israeli soldier, was seized near the Gaza Strip by Palestinian fighters who tunnelled across the border in June 2006.
The fighters continue to demand the release of hundreds of Palestinian prisoners in return for Shalit.