The early morning attack by theman in his mid-20s left bloodstains spattered on the ground outside an entrance to parliament, next door to the famed National Bardo Museum that was the site of a deadly Islamic State group attack in 2015.
A spokesman for the prosecutor's office, Sofiene Sliti, said the assailant set upon the policemen with a knife at around 8:00 am (0700 GMT) stabbing "one in the back of the neck and another at the level of his eyes".
The interior ministry said the assailant was arrested and had confessed to having adopted an "extremist" ideology three years ago. "Killing them (police), he believes, is a form of jihad," it said.
Prosecutors said the assailant -- an unemployed computer science graduate born in 1992 -- was from a suburb of Tunis and did not have a criminal record.
An official at the police station where the man was taken after being detained said the attacker appeared "very aware of what he did".
"He told us: 'This morning, I prayed and I decided to do something for jihad. I saw the policeman in front of me. To me, he's a 'tyrant'. And I did what I did,'" the official quoted the suspect as allegedly saying.
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.
After the latest attack, Tunisia's parliament speaker Mohamed Ennaceur called for "solidarity because the danger threatens the whole of society and the country".
The country has been under a state of emergency since November 2015, after one of those attacks killed 12 presidential guards in the heart of the capital.
In June 2015, 38 foreign tourists, including 30 from Britain, lost their lives in an IS attack on a coastal holiday resort south of Tunis.
In March the same year, another IS attack at the Bardo museum killed 21 foreign tourists and a policeman.
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