Abu Zakaria al-Jamal died of his wounds after a raid.
Israel has now carried out more than 700 strikes on Gaza since launching the offensive a week ago, AFP news agency said.
On Saturday, Israeli artillery shelled the Gaza Strip, witnesses said.
There were no immediate reports of damage or casualties.
The UN warned of a worsening humanitarian crisis in Gaza.
The UN said it believed 25% of more than 400 Palestinians killed by Israeli action so far were civilians.
In his weekly radio address President George W Bush said Hamas was responsible for the latest violence and rejected any unilateral ceasefire that he said would allow Hamas to continue to fire on Israel.
He added that no peace deal would be acceptable without tougher action to prevent Hamas and other groups from receiving weapons.
"There must be monitoring mechanisms in place to help ensure the smuggling of weapons to terrorist groups in Gaza comes to an end," he said.
"I urge all parties to pressure Hamas to turn away from terror and to support legitimate Palestinian leaders working for peace," Mr Bush added.
Israeli air strikes on Gaza continued early on Saturday, with 35 reported. One person was killed as large parts of the American school in north-west Gaza were destroyed.
Israel has threatened to launch a ground offensive. It has called up army reservists, and tanks and troops are massed on the Gaza frontier.
BBC Middle East Editor Jeremy Bowen says a week of bombardment has not been able to stop militant rocket attacks, and Israel now has to decide whether to send in ground troops.
But in a pre-recorded statement broadcast on al-Jazeera TV, Damascus-based Khaled Meshaal said Israel would be making a "foolish mistake" if it sent tanks into Gaza.
Speaking publicly for the first time since Israeli air strikes started a week ago, he said Hamas resistance and infrastructure were intact.
"We will not break, we will not surrender or give in to your conditions," Mr Meshaal said in a speech aimed at the Israelis, the Palestinians and the wider Muslim world.
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