The Palestinian teenagers, aged 15 and 16, were killed when an Israeli strike hit a building they were near in the west of Gaza City, the enclave's health ministry said.
Fifteen people have been wounded across Gaza, the ministry said.
The flare-up came after Israeli troops shot and killed two Palestinians, including a teenager, and wounded hundreds of others in border clashes on Friday, the latest in months of protests.
Israel launches airstrikes on Gaza Strip after border protest bloodshed
The Israeli raids on Saturday involved the "largest daytime operation" carried out by its air force in Gaza since a war in 2014, Israel's military spokesperson Jonathan Conricus told journalists.
Israel's armed forces said dozens of strikes targeted military facilities belonging to the Gaza Strip's rulers Hamas, against which it has fought three wars over the past decade.
In the other direction "more than 60 rockets" were fired at southern Israel from Gaza, the Israeli military said, of which "approximately 10 rockets were intercepted".
On Saturday the Israeli military said it was conducting strikes against Hamas "in response to the terror acts instigated during the violent riots that took place along the security fence" the day before.
Among the main targets was the "Hamas Battalion HQ in Beit Lahia, which includes urban warfare training facilities, (a) weapon storage warehouse, training compounds, command centres, offices and more", the Israeli army said in a statement.
"A weapons manufacturing site and storage facilities housing various types of weapons, including Hamas' naval capabilities" were also hit, the statement added.
The Israeli army said air strikes carried out in the morning hit "complexes used to prepare arson terror attacks and a Hamas terror training facility".
Palestinian killed as Gaza protests against Israel enter fourth month
Hamas spokesperson Fawzi Barhoum said the group was responsible for Saturday's barrage against Israel and that it was carried out "in response to the Israeli air strikes".
"The protection and the defence of our people is a national duty and a strategic choice," Barhoum said.
Palestinians in Gaza have for months been demonstrating against Israel's decade-long blockade of the territory and in support of their right to return to lands they fled or were driven from during the war surrounding the creation of Israel in 1948.
In fresh violence Friday, a 15-year-old was shot dead during the demonstrations and a 20-year-old died later of gunshot wounds sustained during the protest, the Gaza health ministry said.
Since the protests and clashes broke out along the border on March 30, at least 141 Palestinians have been killed by Israeli fire.
The majority of those killed were involved in protests and clashes but others were seeking to breach or damage the border fence.
Israeli forces kill two Palestinians near border as Gaza buries dead
No Israelis have been killed, but officials said one soldier was injured by a grenade on Friday.
Molotov cocktails, flaming tyres and stones were also hurled in the direction of its soldiers according to the Israeli army.
Israel says its use of live fire is necessary to defend its borders and stop infiltrations.
It accuses Hamas of seeking to use the protests as cover for attacks against Israel.
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