More than 12 million boxes of powdered baby milk have been recalled in 83 countries over an outbreak of salmonella.
CEO of the French dairy firm Lactalis, Emmanuel Besnier, confirmed the contamination risk in an interview with French media.
The company's products have been recalled since December when salmonella bacteria was found at a factory.
"We must take account the scale of this operation: more than 12 million boxes are affected," he said.
He promised all families affected would receive compensation.
The firm has faced accusations of covering up the contamination after an outbreak at the plant was detected.
Lawsuits have been filed by parents who say their children fell ill after drinking the formula.
"It is for us, for me, a great concern," he told the Journal du Dimanche.
"There are complaints and there will be an investigation with which we will fully collaborate. We never thought to act otherwise."
Two brands of powdered baby milk, Picot and Milumel, were recalled internationally after reports of children falling sick.
Symptoms of salmonella poisoning include diarrhoea, vomiting, stomach cramps and fever.
Officials in France have reported 35 cases of babies getting salmonella from the powder, as well as one case in Spain and another in Greece.
French investigative publication Le Canard Enchaine reported state inspectors had approved the Lactalis site in Craon, France, in September.
Inspectors had failed to find the salmonella bacteria that had been detected by Lactalis' own tests in August and November.
The results were not reported to the authorities and Lactalis said it was not legally bound to report the contamination.