"We thought we had eliminated terrorism but we hope that terrorism will not bring us down, especially with the bad political climate in Tunisia now", President Beji Caid Essebsi said.
Witness Mohamed Ekbal bin Rajib told Reuters that he was "in front of the theater and heard a huge explosion and saw people fleeing", Ambulances also could be heard rushing to the scene. Hundreds of police cordoned off an area near the landmark Municipal Theatre and the French embassy, while ambulances evacuated the wounded. The station cited a security source it did not name.
According to Radio Mosaique FM, the bomber used a hand-made grenade containing small quantities of explosives.
It said the bomber came from the Mahdia region of eastern Tunisia and was previously unknown to security services, which raided her home after the attack.
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Witnesses say the alleged bomb detonated close to a number of police officers.
Tunisian authorities have been on high alert in recent years following a spate of attacks including a deadly shooting in Tunis' Bardo National Museum in 2015 in which 22 people, including many European tourists, died.
The country has been under a state of emergency since November 2015, when an IS-claimed suicide bombing in Tunis killed 12 presidential guards.