The shooter, identified as Kosta Kecmanovic, drew sketches of classrooms and wrote a list of children he planned to "liquidate", according to senior police official Veselin Milic.
The incident at Vladislav Ribnikar school in central Belgrade left six other pupils and one teacher with injuries.
A father of one pupil said the shooter entered his daughter's classroom, firing at her teacher and then her classmates as they ducked under their desks.
An official said most students were able to flee through a back door.
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