Hisham Ikhtiar is the fourth regime insider to die as a result of the attack at the national security bureau.
The army has fought off an assault by rebels in the Midan area of Damascus.
Meanwhile, Russia’s envoy to France has sparked a row with Damascus after suggesting President Bashar al-Assad was ready to step down.
Alexander Orlov said Bashar al-Assad had, in effect, agreed to step down last month at a conference in Geneva which had planned for a democratic transition.
“Assad nominated his representative to lead the negotiations with the opposition for this transition. That means he accepted to leave, but in a civilized way,” said Alexander Orlov.
His comments triggered an angry response from Syria, where the information ministry said the claims were completely baseless.
The announcement of Hisham Ikhtiar’s death came as the other victims of the bomb attack were buried.
The other three high-profile victims were the defense minister, his deputy who is also Bashar al-Assad’s brother-in-law, and a former defense minister.
The bombing of the National Security Bureau came shortly after rebels declared an all-out assault on the capital, calling it Operation Damascus Volcano.
Eruptions of violence have been seen across the city since Sunday.
In the latest fighting, state media announced the area of Midan had been “cleaned” of “terrorists”.
Rebels said they had withdrawn from Midan after coming under bombardment.
But elsewhere in the country rebel fighters have managed to seize control of several border posts, both on the southern frontier with Iraq and the northern border with Turkey.
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