The al-Qassam Brigades said the fighters tunneled under the Gaza border into Israeli territory near the Sufa crossing east of Rafah. Then they shot five soldiers dead, the group said.
It said three were killed by direct gunshots to the head, while the others suffered bullet wounds in other areas of their bodies.
Only hours earlier, the Israeli army announced the deaths of two soldiers by militants who had breached the Gaza border.
An army statement said those two, Sergeant Adar Bersano, 20, from Neharyia, and Major Amotz Greenberg, 45, from Hod Hasharon, were killed during a clash with a number of militants who infiltrated Israel through a tunnel from Gaza.
The fighters, also affiliated with Hamas' military wing, infiltrated the southern Israeli region of Eshkol near Ein HaShlosha through a tunnel and attacked an Israeli army patrol. more