Hamas identified the man as Fadi Assaf, and confirmed he was a member of their organisation.
In the southern Gaza Strip, the Israeli army shot dead a man approaching the border with Israel.
Hamas identified the man as 35-year-old Mustafa al-Sufi. His family said he was shot from a nearby army watch tower.
On Monday, Hamas said one of its fighters died after being hit by an Israeli air strike near the northern Gaza town of Beit Hanoun.
Israeli soldiers killed three Palestinians and wounded four more on Monday in two separate incidents in the north of the Gaza Strip, medics and the Israeli army said.