Israel killed at least two teenagers and injured 12 civilians in an airstrike on Gaza Saturday evening.
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.
15 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.
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 spokesman Jonathan Conricus told journalists.
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".
The Israeli army said air strikes carried out in the morning hit "complexes used to prepare arson terror attacks and a Hamas training facility".
Hamas spokesman 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 defense 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.
No Israelis have been killed, but officials said one soldier was injured by a grenade on Friday.
Molotov cocktails, flaming tires 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.