Commander Riadh Barrouta, who was knifed in the neck in Wednesday’s attack, “has died”, interior ministry spokesman Yasser Mesbah said.
A second officer was lightly wounded in the forehead in the early morning assault before the attacker in his mid-20s was quickly arrested.
After the attack, the interior ministry said the assailant had confessed to having adopted an “extremist” ideology three years ago.
“Killing them (police), he believes, is a form of jihad,” it said.
Prosecutors on Thursday said the man — an unemployed computer science graduate born in 1992 — appeared to have acted alone and did not belong to any cell, but “intended to join terrorist groups” in neighbouring Libya.
The attacker, who comes from a suburb of Tunis, would be taken before anti-terrorist prosecutors on Friday, said Sofiene Sliti, a spokesman for the prosecutors’ office.
The authorities also said they had launched a probe into the leaking online of a one-minute video of his interrogation.
Since its 2011 revolution, which sparked the Arab Spring, Tunisia’s security forces have faced a series of jihadist attacks that have claimed the lives of more than 100 soldiers and police.
Wednesday’s attack happened next door to the famed National Bardo Museum that was the site of a deadly Islamic State group attack in 2015 that killed 21 foreign tourists and a policeman.
In June the same year, 38 foreign tourists, including 30 from Britain, lost their lives in an IS attack in the coastal holiday resort of Sousse.
Tunisia has been under a state of emergency since November 2015, after another attack killed 12 presidential guards in the heart of the capital.
The attack on the officers comes as Tunisia is debating a contentious proposed law on “protecting” police and soldiers that civil society groups have called “dangerous” for democracy.
Unions representing the security forces have warned lawmakers of protests if they do not pass the bill.
In the wake of the stabbing President Beji Caid Essebsi underscored the “necessity of giving absolute priority” to the legislation “to guarantee the rights” of the police and military.
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