Emmanuel Besnier, the company's CEO, said: "We must take account the scale of this operation: more than 12 million boxes are affected". "They know that everything has to be removed from the shelves".
He also vowed to enhance the sanitary control of the Lactalis products.
That scandal caused distrust in locally produced infant formula and benefited foreign suppliers such as Nestle, Danone and Lactalis.
He promised all families affected would receive compensation.
Besnier did not say how much the damages might amount to.
"It is for us, for me, a great concern", he told the Journal du Dimanche.
Mr Besnier added: "There are complaints and there will be an investigation with which we will fully collaborate".
The European Centre for Disease Prevention and Control said on January 5 that one infant in Spain had fallen ill with a salmonella infection linked to contaminated Lactalis baby milk and another case in Greece was thought to be related. "I think this (further recall) is the strongest guarantee we can give".
His workers nickname him the "invisible man".
Created in 1933 by Besnier's grandfather, Lactalis has become an industry behemoth with annual sales of some €17bn (£15bn).
Two of its brands, Picot and Milumel baby milk, were the subject of chaotic worldwide recalls issued in mid-December after dozens of children fell sick.
The tough measure reflects high-level frustration at the botched handling of the crisis after France's biggest supermarkets - including Carrefour, Auchan and Leclerc - this week said that some Lactalis products subject to recalls in December still found their way onto their shelves.
French dairy group Lactalis have been inundated by parents taking legal action over claims their children were left sick as a result of using the product.