After talks with Lactalis management Le Maire said the company would recall all infant formula milk products made at its Craon factory that were still in warehouses and on store shelves, regardless of the date of manufacture.
Besnier, who was summoned to the French finance ministry on Friday, promised compensation for all the families affected.
He added: "The aim of this radical step is simple: to avoid delays, problems in sorting batches and the risk of human error".
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.
The recall involves some 12 million tins of baby milk. "I think this [further recall] is the strongest guarantee we can give".
In France there have been 35 reported cases of infants getting salmonella as a result of using the products.
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.
An association representing victims says the authorities are underestimating the number of cases. Consumers in China, a fast-growing market for baby food and dairy products, are particularly sensitive to such scares after melamine-tainted baby milk led to the deaths of six children in 2008.
"There are complaints and there will be an investigation with which we will fully collaborate. We never thought to act otherwise", Besnier said.
Lactalis has become an industry giant, with annual sales of 17 billion euros ($20.73 billion) and 18,900 employees across some 40 countries.
With 246 production sites in 47 countries, its list of products also features household names like President butter and Societe roquefort.
Two of its brands, Picot and Milumel baby milk, were the subject of chaotic global recalls issued in mid-December after dozens of children fell sick.
Commenting on the fact that local media reported about the salmonella bacteria detected by Lactalis own technicians at the site in Craon, northwest France, in August and November, the CEO pointed out that the dairy giant had never tried to hide the salmonella outbreak, adding that the company received the information about possible contamination just by December 1. The company said it was not legally bound to report the contamination.