The strike that killed the teenagers unleashed a Hamas' launch toward the Israeli border town of Sderot, where a rocket hit the Buchris family home.
Tel Aviv has most recently ratcheted up its attacks against Gaza, taking it under dozens of airstrikes, while claiming that it is responding to rocket fire from the territory.
Saturday's exchange of missiles and rockets is considered as the biggest since the 2014 Israeli war on the impoverished sliver.
On July 9, Israel closed its only goods crossing with the Gaza Strip in response to the fires.
Israel has been warning Hamas that while it has no interest in exacerbating hostilities, it will not tolerate Gaza militants' continued efforts to breach the border and its campaign of incendiary attacks on Israeli border communities.
Announcing their deaths in the strike on a Hamas facility on Saturday, the Palestinian health ministry said they were walking on a road nearby when they were hit with shrapnel from the huge blast.
On Saturday, the military carried out its largest wave of airstrikes in Gaza since the 2014 war, hitting several Hamas military compounds and flattening a number of its training camps.
On Saturday night, Education Minister tweeted: "The equation by which, after two months of fires and hundreds of rockets on residents of the Gaza Belt, Hamas is dictating [the terms of the] the cease-fire is a serious error".
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Meanwhile, an Israeli army spokesman said that Israeli air forces destroyed sensitive military facilities in the Gaza Strip.
Adnan Abu Amer, a political analyst from Gaza, wrote on his Facebook page "tug-of-war still exists between the Palestinian resistance and Israel until it reaches the cutting point or someone comes along and stops this risky game".
Palestinians reported that two teens were killed in the bombing. The military said Hamas was using it as a training facility and had dug a tunnel underneath as part of its underground network. Most of the recent rockets from Gaza have been fired by smaller factions but Hamas spokesman Fawzi Barhoum said it was an "immediate response" that was meant to "deliver the message".
Thousands turned out for their funerals in Gaza on Sunday, Palestinian news agency Maan reported. Hamas said another Palestinian had died after being shot by Israeli troops during border protests on Friday.
Since late March Palestinian groups in Gaza have held mass protests along the border fence with Israel every Friday.
Twenty-five people were wounded across Gaza, the ministry said.
Israeli officials have repeatedly threatened to launch a military offensive against the Gaza Strip to end Hamas rule, including the resumption of assassinations against Hamas leaders.
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