Four children and an adult were injured in total, officers added.

French President Emmanuel Macron said those badly hurt were "between life and death".

The youngsters are all about three years of age, police said.

A man who spoke to broadcaster BFMTV said he saw first aiders working on "little bodies, three or four years old, perhaps".

Another witness who spoke to the same channel said he saw the attacker assault an elderly man, jumping on him and stabbing him repeatedly.

He said he yelled at police to act.

"It's a place where babysitters and parents take young children to play, and the atmosphere is fantastic," said Yohan, who works at an ice cream parlour just opposite the park.

Interior Minister Gerald Darmanin said a suspect had been arrested "thanks to the swift intervention of police".

The perpetrator is a Syrian man with "legal refugee status", police said.

He is said to be in his 30s. He was not known to the French security services and his motivation is unclear, a source told the Reuters news agency.

Video footage shows two members of the public trying to apprehend him.

BFMTV showed footage of several policemen overpowering an individual in the park.

"He jumped (in the playground), started shouting and then went towards the strollers, repeatedly hitting the little ones
with a knife," a witness who gave his name as Ferdinand told BFMTV.

"Mothers were crying, everybody was running," said another witness, George, who owns a nearby restaurant.

France attack: What we know about stabbing in Annecy playground

Mr Macron said it was an "absolutely cowardly attack in a park" and the "nation is in shock".

Local politician Antoine Armand tweeted that children were attacked in a playground, describing the attack as "abominable".

There is "nothing more abominable than to attack children", French national assembly speaker Yael Braun-Pivet said.

Francois Astorg, the mayor of Annecy, said he was at the scene and will be speaking at lunchtime.

He urged people to avoid the Paquier area of the French alpine town and said his thoughts were with the victims and their families.

In Paris, politicians interrupted a debate to hold a moment of silence for the victims, BFMTV said.