Four young children who were stabbed in a park in Annecy, in France's south-east, are now in a stable condition, officials have told the BBC.
The children, aged between one and three, are being treated in hospital.
Police overpowered and arrested the knifeman after he entered a children's playground to carry out the attack.
A three-year-old British child is among the injured, another is Dutch. Two adults were also hurt, with one in a critical condition.
Police have confirmed that the suspect is a 31-year-old Syrian, who had refugee status in Sweden.
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Regional deputy Antoine Armand described the attack as "abominable" and said authorities were investigating, but knew "very little".
Video footage of the attack uploaded to social media - too graphic for broadcast - shows a little playground, with life going on as normal. Children are running around, and their parents and minders are there.
Then a man comes in with a knife, and very quickly there are screams. He's clearly looking for children to attack - and he attacks one in a pushchair.
French Prime Minister Élisabeth Borne and Interior Minister Gérald Darmanin went to the scene of the attack.
Ms Borne told a news conference that the attacker has "no criminal or psychiatric record".
Annecy prosecutor Line Bonnet-Mathis told reporters that the young victims ranged from 22 months old to three years.
There "doesn't seem to be any kind of terrorist motivation", she said.
Police say the suspect has refugee status in Sweden and recently came to France, leaving behind a wife and three-year-old daughter. In an unsuccessful asylum application last year for refugee status in France, he said he was a Syrian Christian.
During the incident, the attacker invoked the name of Jesus Christ.
A woman identified as his ex-wife told BFM TV that her former partner was a Christian.
"He does not call me for four months. [Our relationship] stopped because we lived in Sweden and he did not want to live in Sweden anymore," she said, adding that he had not previously shown a violent streak.
In recent years, France has become accustomed to knife attacks, often carried out by solitary young men with backgrounds in petty crime and some Islamist connection. It is clear that this attack is of a different nature.
So far, most politicians are being careful not to leap to conclusions, but it is inevitable that the attack will feed into the debate on immigration.
Tributes come in as questions grow
In Annecy tonight, the darkening sky throws shadows across tributes of white roses laid out on the playground wall. A children's drawing, covered with hearts, flutters in the wind. A note, addressed to the four children who were stabbed here, reads: "horror passes; love remains".
And as the flowers began appearing here this afternoon, the children began returning too. By early evening, the playground was once again full of their excitement, the rows of television cameras lined up nearby ignored.
But those who witnessed the attack here, and the dramatic intervention of emergency services, told us they were still shaken and tearful.
This attack on toddlers in a popular tourist spot has shaken France: the horror felt well beyond this town - the motive still a mystery.
As here in Annecy, the tributes and the questions grow.
The suspect is said to have attacked the children - some in pushchairs - as they visited the park, before fleeing the scene and stabbing an elderly man nearby.
Police intervened and the perpetrator was shot in the legs.
France's National Assembly has observed a minute of silence and roads are blocked around the scene of the attack.
President Emmanuel Macron tweeted that the nation was in "shock" over the "act of cowardice".
UK Prime Minister Rishi Sunak, who is on a trip to the US, said: "All our thoughts are with those affected by this unfathomable attack, including a British child - and with their families.
"I've been in touch with President Macron, and we stand ready to offer any assistance that we can."
A witness, Eleanor Vincent, told the BBC she "knew something horrible had happened" as she approached the lake.
"People were going about their business or on their holiday, as I was, and it's just shocking. I have no other way of describing it."
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