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 IDF said it had also targeted a rocket launch squad and a mortar shell launcher in the northern Gaza Strip.
Sporadic Palestinian rocket attacks and incendiary kites from Gaza that have burned large tracts of farmland in Israeli border areas have increased public pressure on Netanyahu for a stronger armed response.
The exchange threatens to spark a further conflagration after weeks of tensions along the volatile border. "This tunnel is part of a Hamas terror tunnel network", a statement by the Israeli army said.
Israeli warplanes targeted an under-construction building in al-Katiba neighborhood in Gaza on Saturday, the Palestinian Health Ministry said.
A Palestinian official who spoke to Reuters on condition of anonymity said Egypt and other worldwide players were holding contacts with Israel and Gaza to restore calm.
The rare strike in the heart of Gaza City blew out windows at a nearby mosque, an art gallery, government offices, a tech start-up company and dozens of houses, leaving light fixtures and wiring dangling. "We have no intention to harm anyone who is not a terrorist", he said.
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The IDF said dozens of rockets had been fired on Israel from within Gaza.
Around 10 other passers-by were wounded, the officials said.
The army added that 91 rockets were allegedly fired from Gaza to the Israeli side since morning. A police spokesman said no hits had been identified in the city.
Hamas called closing the border crossing "a crime against humanity" and the United Nations urged Israel to reverse the decision, warning it could have negative consequences.
Two Palestinian teenagers were killed in an airstrike, while three Israelis were wounded from a rocket that landed on a residential home. Meanwhile, the military says an Israeli officer was lightly wounded by a grenade thrown at him during the near-weekly protests along the border Friday.
However, it appeared that neither Israel nor Hamas were seeking further escalation and there were no reports of serious casualties on either side of the border.
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.