* Salmonella contamination identified at Lactalis plant late 2017
* Scare deepened when retailers said recalled goods still on sale
* Lactalis sells baby milk in Europe, Africa and Asia (Adds more Le Maire quotes, context)
PARIS, Jan 12 (Reuters) - French dairy group Lactalis is widening a product recall to cover all baby milk manufactured by a factory at the centre of a salmonella contamination, Finance minister Bruno Le Maire said on Friday.
The move comes as the government seeks to contain reputational damage to France's strategic agri-business industry in overseas markets. Three dozen children have fallen ill in France and at least one other in Spain.
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.
"The aim of this radical step is simple: to avoid delays, problems in sorting batches and the risk of human error," Le Maire told a news conference on Friday.
In a later statement Lactalis confirmed the extended recall and pledged to find and eradicate the causes of the salmonella contamination.
Implementing the recall will be challenging. Privately owned Lactalis exports its products to dozens of countries across Europe, Africa and Asia.
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.
It has been particularly embarrassing for the government after President Emmanuel Macron pushed food exports during a state visit to China this week.
Salmonella infections can be life-threatening, particularly for young children, and the recall risks damaging Lactalis in China. 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.
That scandal caused distrust in locally produced infant formula and benefited foreign suppliers such as Nestle, Danone and Lactalis.
"I cannot guarantee that right now there isn't a single tin of baby milk left on a shelf in a giant warehouse or in a pharmacy," Le Maire said. "I think this (further recall) is the strongest guarantee we can give."
Le Maire did not say what volume of baby milk could be involved beyond the more than 12 million items already recalled last month.
The European Centre for Disease Prevention and Control said on Jan. 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.
A judicial investigation is taking place in France over the contamination and a group of French parents of affected infants said on Friday that they were considering a joint lawsuit.
(Reporting by Gus Trompiz and Richard Lough; Editing by David Goodman)