It is still unclear how many Britons have been caught up in the massacre, caused when French-Tunisian father-of-three Mohamed Lahouaiej Bouhlel drove the hired vehicle into crowds celebrating the French national day, resulting in at least 84 deaths. Bouhel was subsequently killed in a shoot-out with police.
A total of 85 people are still in hospital as a result of their injuries, with 18 in a life-threatening condition, Ms Touraine said.
Speaking to reporters in Nice on Sunday, she said while scores of people who were taken to hospital have been released, some may need further medical treatment as their injuries heal.
Crying relatives hugged each other outside the Hopital Pasteur on Sunday as they learned news of their loved ones.
A medical student who volunteered to help at the hospital said he had been one of many who helped with the bodies.
The 21-year-old, who did not wish to give his name, told the Press Association: “It was all about helping identify and move bodies, dead bodies.”
Six people remain in custody following the attack on the Promenade des Anglais in Nice on Thursday.
A seventh person - Bouhlel’s estranged wife - has been released from custody. She is the mother of Bouhlel’s three children, and was in the process of divorcing him.
The promenade reopened around 36 hours later, as holidaymakers walked along the waterside stretch, which is lined with hotels and restaurants, while police officers kept watch.
Flowers, cards and messages of solidarity marked the spots where bodies had been left strewn on the road in the aftermath of the massacre.
Candles burned late into the night on Saturday as crowds gathered once again in memory of those killed and injured.
The Islamic State (IS) group has claimed Bouhlel was “a soldier” acting on its behalf by committing the murders.
The IS claim of responsibility came after the French authorities said Bouhlel had no known links with terrorists, unlike those behind previous attacks in Paris.
And a former neighbour said the 31-year-old had never spoken about extremism.
Speaking outside the high-rise block of flats on Boulevard Henri Sappia, where the suspect had previously lived with his family, Samiq, 19, who did not want to give his surname, said: “I never heard him speak about extremism, I cannot believe that he was a member of Islamic State.”
He said people thought Bouhlel had psychological problems.
“He was a little bit crazy,” Samiq said, but he added that he was shocked by what had happened.
The apartment on Route de Turin where Bouhlel was believed to be living before the attack was raided by police, and a view through the keyhole showed items including what appeared to be boxes of medication and a strip of tablets.
The driver’s father has said that Bouhlel had received psychiatric treatment in the past.
A neighbour and her young daughter said he lived a reclusive life, failing to respond when they said hello.
Interior minister Bernard Cazeneuve, who announced 12,000 extra police reserves are being called up alongside the 120,000 police and soldiers already in place across the country, said Bouhlel appeared to have been radicalised only recently.
Speaking in St Peter’s Square in the Vatican on Sunday morning, Pope Francis prayed for the end of “terror and death” of innocents as he expressed closeness to families and all of France mourning the loss of lives.
He told the public that “sorrow is great in our hearts” and prayed that God “disperse every plan for terror and for death, so that no man dare spill more blood of his brother”.
The Pope then invited those in the square to join him in silent prayer for the victims and their families.
It came as French prime minister Manuel Valls said it was “without a doubt” that Islamic State was involved in the attack.
Mr Valls, in an interview with the Journal du Dimanche newspaper, said that authorities “now know that the killer radicalised very quickly”.