A member of the armed wing of Hamas died in an exchange of fire between Palestinian fighters and an Israeli military, emergency medical services said.
Hamas said in a statement that its fighters had fired anti-tank rockets at the troops.
An air raid on the village of Beit Lahiya in central Gaza reportedly targeted a Hamas base.
On Thursday, an Israeli man was killed in a mortar attack by Gaza fighters, triggering an air raid on the territory that left a four-year-old Palestinian girl dead.
The girl's mother and another woman were wounded in the air raid by an Israeli drone which the Israelis said had targeted Palestinian armed groups.
The girl and her mother were outside their house near Khan Yunis in southern Gaza when a drone fired a missile, witnesses said.
The Khan Yunis hospital identified the girl as Aya al-Manjar and said her mother was critically wounded.
An Israeli military spokeswoman confirmed the attack, saying: "The air force conducted a raid and fired at Palestinian gunmen."
She said the attack targeted the area from which Palestinian fighters had earlier fired rockets that hit a kibbutz, or commune, in southern Israel, killing the Israeli man and wounding several.
Clashes between Israeli forces and armed Palestinian groups have continued in and around the tiny Palestinian territory despite efforts by Egypt to mediate a truce.
Ayman al-Zawahiri, al-Qaeda's number two, issued a new internet message on Wednesday urging fighters to escalate attacks on Israel over the crippling siege of the territory it imposed after Hamas seized control almost a year ago.