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At least one Palestinian was killed on Wednesday when Israel launched air strikes across Gaza, after a rocket was fired from the besieged enclave at an Israeli city. 

Israel said at least 20 "military targets" were hit in the air strikes, with Gaza's Palestinian health ministry naming a 25-year-old victim - Naji al-Zaaneen - from the bombing.

The Israeli army produced a video showing a man near the border preparing a rocket launch when he was targeted in an air strike.

It follows rocket fire on the southern Israeli city of Beersheba, early Wednesday morning.

"At 4am, Israelis in the city of Beersheba were running to bomb shelters after a rocket was launched from the Gaza Strip at Israel," the Israeli army tweeted, before the air strikes on the besieged Palestinian enclave.

Defence Minister Avigdor Lieberman ordered the closure of both of Israel's border crossings with Gaza on Wednesday following the attacks.

It also reduced the permitted fishing zone along the Gaza coast to three nautical miles.

Gaza has been under siege for 11 years, creating a major human catastrophe in the enclave.

Qatar struck a deal to allow fuel to be imported into Gaza, with hopes that the punishing blockade might be eased and conditions for Palestinians living in the strip improved.

Protesters on the Gaza border have also been targeted by Israeli live-fire, with at least 205 Palestinians killed by bullets and tear gas since protests began on 30 March.