Hamas was responsible for the mortar fire on the Kibbutz Kfar Aza that killed a 40-year-old man on Friday, according to a Hamas radio report.
Abu Obeida, a spokesman for Hamas' military wing, said militants had targeted a military position.
Asked if the deadly attack wouldn't make it more difficult to conclude a truce, he replied, "We will continue to fire until the last moment" before a truce is completed.
"Hamas is clearly in control of the Gaza Strip and responsible for all hostile fire into Israel. We hold it accountable for today's attack and the murder of our civilians," said David Baker, an Israeli government spokesman.