MENA said the fight late on Monday started when a shop owner opened fire with his automatic rifle and killed two people who spread their merchandise on the ground outside his shop.
The agency said colleagues of the two set fire to the man's shop, where he and 12 of his workers were taking cover, killing them all.
The gunfight and the revenge arson in the old Cairo neighbourhood of el-Moski are the latest signs of lawlessness that has struck Egypt during two years of political turmoil.
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