An Islamic Jihad official identified the dead man as a member of his group.
Hamas officials and residents said the clashes broke out after gunmen from Islamic Jihad tried to abduct a member of Hamas in the city of Rafah in the southern Gaza Strip.
Hamas forces foiled the attempt and seized 15 members of Islamic Jihad, including its top commander in the town, they said.
Sunday's clash came one day after three Palestinians died in fighting between Hamas forces and members of a clan loyal to President Mahmoud Abbas's Fatah group, one of the deadliest since the Islamist group seized the Gaza Strip after routing Abbas's forces in June.
Hamas losing ground?
Hamas' main internal achievement after taking over the Gaza Strip last June appeared to be the halt in the ongoing clashes between rival Palestinian factions, but the past few days have raised fears that the security anarchy may be returning to the Strip.
The Hamas movement recently announced that it had uncovered a network of Fatah members responsible for a series or explosions across the Strip targeting senior Hamas officials, particularly members of the special security force, and the force's headquarters.
Over the past week, Hamas members even clashed with members of the Popular Resistance Committees, considered their allies.
Ali Waked contributed to the report