An IDF tank destroyed a Hamas watchtower after shots were fired at Israeli soldiers near the Gaza border.
The Israeli strike reportedly hit a graduation ceremony of al-Qassam at a Hamas military base with senior Hamas figures in attendance.
Hamas issued a statement threatening to retaliate for the deaths.
The incident took place amid Egyptian efforts to broker a cease-fire between Israel and the Palestinian militant group, which controls the coastal strip.
According to the group, Israeli forces have killed more Palestinian children since January this year than in any previous year of the past decade, outside of large-scale Israeli military offensives.
Israel's security cabinet discussed the proposal on Sunday, but afterwards ministers said only that the Israeli military was "prepared for any scenario".
Hamas warned Israel that it would pay for the attack, without elaborating.
One Israeli soldier has been shot dead by a Palestinian sniper during the same period, while incendiary devices attached to balloons and kites launched by Palestinians have sparked hundreds of fires in southern Israel, burning some 3,000 hectares (7,400 acres) of forest and farmland.
The "Great March of Return" protests sought the right of Palestinian refugees and their descendants, who according to the United Nations make up around two-thirds of Gaza's population, to return to their homeland inside what is now Israel.