No injuries or damage were reported.
A bomb disposal crew carried out three controlled explosions at about 4:30 am (0230 GMT) today to destroy the device, which was found in a backpack placed in a plastic container at the building's entrance.
Authorities were alerted following an anonymous call to a newspaper at about 1 am in which the caller said a bomb was to explode in 40 minutes.
Police said it was not immediately clear why the device did not explode. Anti-terrorism police were leading the investigation and forensic experts were examining the remnants of the backpack and its contents.
A number of small domestic extremist groups are active in Greece, usually carrying late-night attacks that rarely cause injuries.
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