The Israeli military has carried out its largest daytime air strike campaign in Gaza since the 2014 war, as Hamas militants fired dozens of rockets into Israel throughout the day.

Two Palestinian teenagers were killed in an air strike in Gaza City, while three Israelis were injured by a rocket that landed on a residential home.

Israel said it was focused on hitting military targets and warned Gaza civilians to keep their distance from certain sites.

But even before the report of casualties, the intense tit-for-tat air strikes and rocket barrages still marked a significant flare-up after a long period of a generally low-level, simmering conflict.

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Israeli soldiers stand next to cars Palestinians said were set on fire by Jewish settlers (Majdi Mohammed/AP)

Lt Col Jonathan Conricus said the latest Israeli sortie, the third of the day, struck some 40 Hamas targets including tunnels, logistical centres and a Hamas battalion headquarters.

He said the escalation was the result of the sustained Hamas rocket attacks, its fomenting of violence along the border and its campaign of launching incendiary kites and balloons that have devastated Israeli farmlands and nature reserves.

“Our message to Hamas is that we can and will enhance the intensity of our effort if needed,” he said.

“What Hamas is doing is pushing them ever closer to the edge of the abyss… Hamas will have to understand that there is a price to be paid.”

Later, witnesses reported that Israeli warplanes dropped four bombs on an unfinished building near a Hamas police and security compound in Gaza City, reducing the old structure to rubble. The four-storey building is adjacent to a public park.

Gaza’s Health ministry said two teenagers were killed in the strike and 10 others injured.

Striking in the heart of Gaza City is typically only seen during full-blown conflicts like the 2014 war, and observers fear it could signal that a further escalation may be in store.

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Smoke and fire from an Israeli air strike rise over Gaza City (Hatem Moussa/AP)

The Israeli military had no immediate reaction to that strike but said it had targeted a separate high-rise building in the northern Gaza Strip that was used as a Hamas urban warfare training facility. It said a tunnel was dug under the building.

Shortly after, Israeli medical officials said three Israelis were injured by a rocket that landed on a house in southern Israel.

It said paramedics in the southern city of Sderot were treating a 52-year-old man with a chest wound, a 17-year-old girl with a face wound and a 20-year-old woman with injuries to her limbs.

Sirens wailed overnight and throughout most of the day on Saturday in southern Israel as waves of rockets and mortars were launched from Gaza amid the air strikes.

The military said it identified about 60 launches of rockets and mortars from Gaza towards Israeli territory, of which about 10 were intercepted by the Iron Dome aerial defence system.

As a precaution, the military shut down a popular beach in southern Israel and placed limitations on gatherings of large crowds. Israeli police said four of the projectiles caused damage.