Thursday night's attack at peak holiday time on the Riviera plunged France into new grief and fear just eight months after extremist gunmen killed 130 people in Paris.
French Health Minister Marisol Touraine said the 18, including one child, were in a critical condition, while about 85 people in total were still hospitalised.
The attacks, along with one in Brussels four months ago, have shocked Western Europe, already anxious over security challenges from mass immigration, open borders and pockets of religious radicalism.
France reels from second ‘terror’ attack in eight months
Authorities have yet to produce evidence that the 31 year-old delivery driver, Tunisian Mohamed Lahouaiej Bouhlel, shot dead by police, had any actual links to Islamic State. The Islamist militant group claimed the attack though, and Valls said there was no doubting the assailant's motives.
"The investigation will establish the facts, but we know now that the killer was radicalised very quickly," Prime Minister Manuel Valls said in an interview with newspaper Le Journal du Dimanche.
As of Sunday no evidence had been produced to show how he underwent that rapid transformation from someone with no apparent interest in religion.
Relatives and friends interviewed in Nice painted a picture of a man who at least until recently drank alcohol, smoked marijuana and according to French media even ate pork, behaviour that would be unlikely in a devout Muslim.
A report in the Nice Matin newspaper on Sunday said investigators had found no radicalisation material in his flat, although they were still looking at his telephone and his computer.
Speaking from his home town in Tunisia, Bouhlel's sister told Reuters he had been having psychological problems when he left for France in 2005 and had sought medical treatment.
'Reviewing our own safety' after Nice attack, says London mayor
As authorities were trying to better understand his motives, two more people, a man and a woman close to Bouhlel, were arrested in Nice early on Sunday.
Three others arrested previously were still being held, but Bouhlel's estranged wife was released without charges after being held since Friday.
The Amaq news agency affiliated with the militant group said on Saturday in claiming the attack that Bouhlel "was one of the soldiers of Islamic State".
The group, which is under military pressure in its Irag and Syria strongholds from forces opposed to it, considers France a key target given its military operations in the Middle East, and also because it is easier to strike than the United States, which is leading a coalition against it.
France is also home to Europe's biggest Muslim population, and has been criticized in some quarters for fostering racial, ethnic and religious disharmony through its strict adherence to a lay culture that allows no place for religion and ethnicity in schools and civic life.
Long and open borders with neighbouring countries also make it an easy target for attackers who want to melt away afterwards.
Security failures?
Valls defended France's record on attacks, saying security services had prevented 16 over three years and said the group's modus operandi of cajoling unstable people into carrying out attacks with whatever means possible was difficult to combat.
"Daesh gives unstable individuals an ideological kit that allows them to make sense of their acts...this is probably what happened in Nice's case," Valls said, referring to the Arabic acronym for Islamic State.
Despite mounting criticism from the conservative opposition and the far-right over how President Francois Hollande's Socialist government is handling security, Valls said there was no such thing as zero risk and that new attacks would occur.
"I've always said the truth regarding terrorism: there is an ongoing war, there will be more attacks. It's a difficult thing to say, but other lives will be lost."
With presidential and parliamentary elections less than a year away, French opposition politicians are increasing pressure and seizing on what they described as security failings that made it possible for the truck to career 2 km (1.5 miles) through large crowds before it was finally halted.
After Thursday's attack, a state of emergency imposed across France after the November attacks in Paris was extended by three months and military and police reservists were to be called up.
Interior Minister Bernard Cazenueve on Saturday called on "patriotic citizens" to become reservists to help relieve exhausted security forces.
But the measures appear to have done little to temper concerns. Highlighting the "serious deficiencies" in protecting French citizens, National Front leader Marine Le Pen demanded that Cazeneuve resign.
"Anywhere else in the world a minister with such a terrible record - 250 deaths in 18 months - would have resigned a long time ago," she told reporters.
Christian Estrosi, president of the wider Riviera region and a a security hardliner, accused the government of failing completely in Nice.
"When the interior minister says there were enough police, it constitutes a blatant lie," he told i-Tele television. "He said there were 64 national policemen on duty. It's false and the investigation will show it."
Valls has said there were no failures, although Cazeneuve acknowledged on Saturday that the truck had avoided the police vehicles blocking the way to the promenade by mounting a kerb.
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