Abu Ubaida, a spokesman for Hamas's armed wing, said on Wednesday that they had only responded to shooting from the al-Aqsa commander's house.
"This is just a ploy to regain international hand-outs with smoke and mirrors"
LeotheIsaurian, Detroit, US
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He said a Fatah fighter was preparing to fire a rocket-propelled grenade when it exploded in his hands, killing him and wounding the others.
But Abdel Hakim Awad, a Fatah spokesman, charged that the attack was planned and said there would be "grave consequences" if Hamas mounted any more such attacks.
It was the first deadly clash since Fatah and Hamas formed a unity cabinet on Saturday.
Hamas said it suspected Fatah of seizing one of its political leaders, and a lecturer at the Hamas-linked Islamic University, in Gaza City.
Fatah had no immediate comment.
In his first act after swearing in the new government, Mahmoud Abbas, the president, appointed Hamas's long-time foe, Muhammad Dahlan, as national security adviser, angering the movement.
And over Fatah objections, Hamas has pushed ahead with plans to double the size of its security forces to 12,000 members.
By nightfall, Hamas and Fatah representatives said they had agreed to hold their fire and had withdrawn fighters from the streets.
The unity deal between the two groups has eased a Western diplomatic embargo of the Palestinian government.
Brushing aside Israeli appeals to shun the government, the EU and the UN sent their Middle East envoys for talks with non-Hamas ministers.
The contacts followed a meeting on Tuesday between a senior US diplomat and Salam Fayyad, the Palestinian finance minister.
The meetings marked a move back to at least some engagement between the government and the Quartet of Middle East mediators - the UN, US, EU and Russia - but a year-old ban on direct aid remains.
Despite the direct aid embargo, however, the UN says about $1.2bn in foreign aid reached the Palestinians last year, up from an estimated $1 bn in 2005.