French President Emmanuel Macron, accompanied by his wife, Brigitte, traveled to the French Alps Friday to be with families of the victims stabbed Thursday in a lakeside park in the city of Annecy.
The couple's first stop was a hospital in the French city of Grenoble, where three of the four young children are receiving treatment.
Government officials said all four children have undergone surgery and are "under constant medical surveillance," with one child in critical condition.
The fourth child is being treated in Geneva, in Switzerland.
It is not immediately clear whether the president and his wife will go to Geneva.
A man stabbed the children and two adults at the park Thursday morning in an attack Macron said shocked the country.
All four children suffered life-threatening knife wounds, lead prosecutor Line Bonnet-Mathis said. The youngest is 22 months old, two are 2 years old and the oldest is 3, the prosecutor said.
Police quickly detained the suspect - a 31-year-old Syrian national. French Prime Minister Elisabeth Borne said the suspect has refugee status in Sweden.
"The nation is in shock," Macron tweeted. He described the assault as an "attack of absolute cowardice."
Video appearing to show the attack circulated on social media. In the video, a man in dark glasses with a blue scarf covering his head wielded a knife as people screamed for help.
One woman tried to fend off the attacker in the enclosed play park, but she could not stop him from leaning over her stroller and stabbing downward multiple times.
Two of the young victims were French. The other two were tourists, one British, the other Dutch.
Two adults also suffered knife wounds. One of the adults was also injured by a shot fired by police as they were arresting the suspect, Bonnet-Mathis said.
In Paris, lawmakers paused a debate to hold a moment of silence for the victims.
The National Assembly president, Yaël Braun-Pivet, said, "There are some very young children who are in critical condition, and I invite you to respect a minute of silence for them, for their families, and so that, we hope, the consequences of this very grave attack do not lead to the nation grieving."
"Nothing more abominable than to attack children," Braun-Pivet said on Twitter.
Some information in this report came from Reuters and The Associated Press.