In a statement, the ministry said that Hassan Shalabi, 14, and Hamza Ashtiwi, 18, had been "martyred by Israeli forces".
The Health Ministry said the soldiers killed a child, identified as Hasan Eyad Shalabi, 14, from the Nusseirat refugee camp, in central Gaza, after shooting him with live fire in the chest, east of Khan Younis, in the southern part of the Gaza Strip.
Israeli security forces arrested a Palestinian man on Saturday suspected of killing an Israeli woman found dead two days ago in a forest on the outskirts of Jerusalem, police said.
During the same period, two Israelis were killed in the context of Gaza hostilities while another 52 suffered injuries, the report said.
The Israeli military said it had opened fire in response to explosives and rocks hurled at the border fence.
The Israeli army declined to comment on the death, but said that 8,200 "rioters and demonstrators" had been protesting along the frontier.
The only options previously available to Palestinians in the Netherlands were "Israel" and "unknown" - the latter addad as an option in 2014 because Palestinians had protested against putting Israel as their place of birth.
Earlier this week, Israel began reinforcing its Gaza security fence with a galvanized steel barrier 65 kilometers long (40 miles) and six meters high (20 feet). At least 295 Palestinians were and about 6,000 wounded during the 46 weeks of clashes. At that moment, the boy was struck in the head by a tear gas canister fired directly at protesters by Israeli forces.
The militant Hamas group demands an end to the Israeli-Egyptian blockade imposed on the territory since 2007.
The West Bank was hit by a bout of unrest in December as tensions eased in the Gaza Strip. but they later eased in the West Bank too.