The bus was hit on the busy Mohamed 5 Boulevard on Tuesday evening, prompting President Beji Caid Essebsi to impose a nationwide state of emergency.
The Islamic State of Iraq and the Levant (ISIL) claimed responsibility for the attack in a statement shared on its supporters’ social media accounts on Wednesday.
It is the third major attack in Tunisia this year following the gun assaults on a Sousse resort hotel in June and the Bardo National Museum in Tunis in March.
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“According to the preliminary details, the attacker was wearing a bag on his back,” Hichem Gharbi, a presidential security official, told local Shems FM radio.
“He had on a coat and was wearing headphones. He blew himself up just getting into the door of the bus with military explosives.”
It was also the first suicide bombing in Tunis.
In October 2013, a bomber blew himself up on a beach in Sousse, while an al-Qaeda suicide bomber attacked the synagogue in Djerba, killing 21 people.
“This is an evolution in the behaviour of the terrorists,” said Habib Essid, Tunisian prime minister, after an emergency security meeting.
“This time they attacked a symbol of the state and in the heart of the capital.”
Troops and armed police patrolled the streets and set up checkpoints searching vehicles and pedestrians.
At Tunis International Airport, security forces were allowing in only passengers who were travelling.