The Health Ministry in Gaza said the teenagers, aged 15 and 16, were killed by shrapnel from an Israeli attack on the training facility. In the 100 days since the weekly rallies began, at least 138 people, including 19 minors, were killed.
Earlier, the military said its jets targeted a Hamas tunnel in the southern Gaza Strip as well as other military compounds. Two hours earlier, two mortar shells fired from Gaza struck southern Israel, causing neither injury nor damage.
Some of the projectiles were intercepted by Israel's Iron Dome system, but police said three people had been wounded in the southern town of Sderot. "It is Hamas, not Israel, that's deciding when to escalate and when to back down". The Israelis retaliated with live fire, killing a Palestinian teen and injuring 220 others throughout the day, Wafa reported.
"The IDF has struck Hamas with the hardest blow since Operation Protective Edge and we will increase the strength of our attacks as necessary".
"After consultations with the defence minister, the chief of staff and Israel's top defence officials, we decided on powerful action against Hamas terrorism", Netanyahu said in a video statement.
Fawzi Barhoum, Hamas spokesman, said "the protection and the defence of our people is a national duty and a strategic choice". Militants have tried repeatedly to break through the border fence, attacked soldiers, and destroyed thousands of acres of farmland and nature reserves in southern Israel with kites and balloons outfitted with firebombs and explosives.
Clashes in eastern Gaza with the Israeli army forces resumed Friday as part of rallies and protests organised since March 30.
No Israelis have been killed.
There have also been hundreds of fires at Israeli farms caused by kites and balloons carrying firebombs from Gaza, leading to political pressure on the government and military to take action against Hamas.
Hamas called the move a "crime against humanity", with Gaza already suffering from deep poverty and worsening humanitarian conditions. The embassy move enraged Palestinians, who want East Jerusalem as capital of their future state.
Saturday's fighting between Israel and Hamas was the worst since the 2014 Gaza war, which killed 2,251 Palestinians, about half of whom fighters for various terror factions.
According to the IDF, a military officer was lightly wounded by a grenade thrown at the border on Friday.
"The IDF is determined to continue to defend citizens of Israel and is prepared for a variety of scenarios that may intensify", the army said. A second Palestinian protester died of his wounds on Saturday.
Sirens wailed overnight and throughout most of the day Saturday in southern Israel as waves of rockets and mortars were launched from Gaza amid the airstrikes.
"A tunnel was dug under the building and used for underground warfare training".