Cross-border exchanges between Israel and Gaza have increased in recent days, and Israel said today it holds Islamist movement Hamas responsible, as rulers of the Palestinian enclave, for any fire directed from there at the Jewish state.
Palestinian medics named the dead girl as Hala Abu Sabikha from a refugee camp in the central Gaza Strip.
They said at least six other people had been wounded in the series of tank and air strikes throughout Gaza, including on militant positions.
"The sites included a weapon-manufacturing facility and a terror infrastructure in the southern Gaza Strip, a terror site and another terror infrastructure in the central Gaza Strip and a concealed rocket launcher in the northern Gaza Strip."
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The army said the attacks were in retaliation for the shooting of an Israeli man engaged in maintenance work on the northern Israel-Gaza border fence by a Palestinian sniper.
A police spokeswoman identified him as Saleh Abu Latif, 22, a Bedouin from the southern town of Rahat.
Just ahead of the air strikes, Prime Minister Benjamin Netanyahu warned that Israel would respond "forcefully" to the attack.
And Defence Minister Moshe Yaalon stressed that "in Gaza, Hamas is ruler, and we hold it responsible for the shooting today from the Strip and the rocket launches in the past two days at Israel."
"I advise Hamas to not test our patience," he said in a statement. "If there won't be quiet in Israel, there won't be quiet in Gaza either."