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

French President Emmanuel Macron said an adult was "between life and death".

The youngsters are all about three years of age and the attacker was a man, police said.

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

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".

The assailant was a Syrian asylum seeker, BFM TV reported.

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 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.