The bombings were said to have "some of the hallmarks" of 1,200 prisoners who escaped from a city jail during the weekend, the BBC reported Sunday.
Anti-tank explosives placed under a car caused one blast near a courthouse Sunday, said Mohamed al-Hijazy, a spokesman for the city's military command center.
Witnesses said the building sustained major damage.
The second explosion occurred in front of a building used by the justice ministry, al-Hijazy said.
He added the explosions had "some of the hallmarks of other similar incidents" committed by the prisoners who escaped Saturday.
The explosions occurred at the time when residents were breaking their Ramadan fasts, so few people would have been on the streets.
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