Medics named one of the dead men as Fuad Mauf, 22, an activist of the Democratic Front for the Liberation of Palestine (DFLP).
DFLP fighters said they fired rocket-propelled grenades and machine guns at the Israeli forces and detonated bombs they had planted previously near the border fence.
Local residents said Israeli tanks had entered the area, which the army denied.
"The army has found 40 explosives planted in that area since the November ceasefire," an army spokesman said.
Ayman Mohyeldin, Al Jazeera's correspondent in Gaza, said: "Palestinian sources say... last night the Israeli army entered the eastern part of Gaza and Palestinians tried to prevent the tanks form entering any further. There was an exchange of gunfire and a member of the DFLP was killed by an Israeli attack helicopter."
"The Israeli army says that was not the case. They say they believed the men were planning an attack and had observed suspicious activity. As a result they say they were compelled to enter to respond to the preparation."
Peretz allows 'operations'
Amir Peretz, the Israeli defence minister, authorised the army on Monday to carry out operations against fightersGaza, despite the ceasefire agreement between Israel and the Palestinians.
Some Palestinian groups have carried on firing rockets into Israel from Gaza despite the truce, and Peretz said the Jewish state would "not allow the continued strengthening and arming" of fighters in the coastal strip.
A local leader of al-Aqsa Martyrs Brigades was wounded by Israeli fire on Saturday in the West Bank, residents said.
Zakaria al-Zubeidi, an al-Aqsa commander from the Jenin refugee camp, was shot in the shoulder by Israeli troops, members of the group said.
"He [al-Zubeidi] was taken to a safe place where he was treated. He is okay," a member of al-Aqsa said.
Ali al-Sumodi, Al Jazeera's correspondent in Jenin, said: "This is the fifth Israeli assassination attempt targeting al-Zubaidi since the beginning of the Israeli army's campaign to pursue him following the Jenin refugee camp battle in April 2002.
"Al-Zubaidi's mother, brother and cousin were killed in the 2002 massacre. Israeli forces have demolished his house and detained many of his relatives, including two brothers.
"Israel claims al-Zubaidi's name is on top of its list of wanted activists for involvement in anti-Israeli activities."