Counterterrorism investigators are working to determine whether the man who stabbed five people in a busy neighbourhood in the heart of the French capital Saturday night had any help.
The attacker killed a 29-year-old man and wounded four others before being shot by police.
Witnesses reported hearing the man shouting Allahu akbar, the Arabic phrase for God is great, during the attack.
The Islamic State group claimed the attacker was one of its fighters but provided no evidence or details about his identity.
The assailant had been on a nationwide database of thousands of people suspected of links to radicalism, according to a judicial official. Extremists behind multiple attacks in France in recent years were also on radical watch lists.
The official said on Sunday the assailant, born in 1997, had French nationality but was born in the largely Muslim Russian republic of Chechnya, where extremism has long simmered.
The official wasn't authorised to be publicly named speaking about an going investigation.
The man had no record of arrests or criminal activity, and didn't know his victims, Interior Ministry spokesman Frederic de Lanouvelle told The Associated Press.
The attacker targeted five people and then fled, according to Paris police and a witness. When police officers arrived minutes later, he threatened them and was shot dead, according to police union official Yvan Assioma.
Bar patrons and opera-goers described surprise and confusion, and being ordered to stay inside while the police operation was underway on rue Monsigny in the lively 2nd arrondissement, or district, of the French capital.
'He looked crazy'
Witnesses described dramatic scenes as the knifeman struck.
"I was taking orders and I saw a young woman trying to get into the restaurant in panic," Jonathan, a waiter at a Korean restaurant, told AFP.
The woman was bleeding and a young man fended off the assailant who then ran away, he said.
"The attacker entered a shopping street, I saw him with a knife in his hand," he said. "He looked crazy."
Milan, 19, said he saw "several people in distress" including a woman with wounds to her neck and leg.
A 29-year-old man was killed in the attack, while a Luxembourg man aged 34 and a woman of 54 were seriously wounded and rushed to hospital.
A 26-year-old woman and a man of 31 were slightly wounded, though officials said all the wounded were out of danger.
China's Xinhua news agency reported that a Chinese citizen was among the injured, citing the Chinese embassy in Paris.
A police official said the assailant didn't have identity documents with him during Saturday's attack but was identified thanks to DNA.
The four people injured are out of life-threatening danger, Interior Minister Gerard Collomb said.
Collomb held a special security meeting on Sunday to address the Paris attack, whose motive was unclear.
The Islamic State group's Aamaq news agency said the assailant carried out the attack in response to the group's calls for supporters to target members of the US-led anti-IS military coalition.
French President Emmanuel Macron tweeted: "France has once again paid the price in blood but will not give an inch to the enemies of freedom."
France's military has been active in the coalition since 2014, and IS adherents have killed more than 200 people in France in recent years.
'No such thing as zero risk'
The attack again underscored the difficulty in keeping tabs on suspected extremists by police facing thousands of potential risks, either from homegrown radicals or recent arrivals.
The FSPRT watchlist alone has nearly 20,000 people, of whom about half are under active surveillance.
"What good does this S file do if we don't use it to get these ticking time bombs off French soil," far-right leader Marine Le Pen posted on Twitter.
But Griveaux defended the government's efforts, saying it had foiled 22 planned terror attacks over the past 15 months.
"Unfortunately, there's no such thing as zero risk, and those who say that measures taken out of a hat would fix this problem are lying," he said.
France has suffered a series of major Islamist attacks including the massacre at the satirical newspaper Charlie Hebdo, the November 2015 attacks that killed 130 in Paris, and the 2016 Bastille Day truck attack in Nice that killed more than 80.
Most of the attacks have either been claimed by the Islamic State group or been carried out in its name.
Thousands of French troops remain on the streets under an anti-terror operation known as Sentinelle, patrolling transport hubs, tourist hotspots and other sensitive sites.
