Prosecutors in France are treating the knife attack that killed one person in Paris and injured four others as a terrorist incident.
Two of the wounded in the attack are in a serious condition but do not have life-threatening injuries.
The assailant who killed a 29-year-old man in a central Paris knife attack on Saturday night was a French citizen born in the Chechnya region of Russian Federation in 1997, judicial sources said on Sunday.
Macron said he salutes the courage of the police who "neutralied the terrorist" in the Paris knife attack, according to a tweet from his official account.
His parents have been taken into custody.
Paris police officers evacuated people from some buildings in the Right Bank neighbourhood after the attack, which happened on rue Monsigny at about 9 p.m. (1900 GMT.) Bar patrons and opera-goers described surprise and confusion in the immediate area.
In the attack one person was killed and four were injured.
The watch list contains anyone suspected of being a radical, including potentially unsafe religious extremists but also leftist and far-right activists.
The bloodbath follows a series of ISIS and Al Qaeda attacks in France which has seen nearly 250 killed by terrorists since early 2015.
That list now has almost 20,000 people, of whom about half are under active surveillance.
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Shocked tourists and residents looked on from behind a security perimeter set up by the police.
Islamic State has said it is behind the attack, calling the knifeman one of its "soldiers".
"We didn't know what was going on, we were quickly moved inside the bar, I went outside and I saw a man lying on the floor".
Islamic State claimed responsibility for Saturday's attack, but did not provide proof for its claim.
My gratitude to the police force who neutralised the assailant.
Molins said the anti-terrorism section of the prosecutor's office was handling the investigation.
French Interior Minister Gérard Collomb praised police for their "cool response".
After the attack, French President Emmanuel Macron said that "France once again pays the price of blood" and that the country would not cede to "enemies of freedom".