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BERLIN, Oct 13 (Reuters) - Volkswagen VOWG_p.DE will cut investment at its biggest division by 1 billion euros ($1.1 billion) a year and speed up cost cutting, the carmaker said on Tuesday, as it strives to cope with fallout from its cheating of diesel emissions tests.

The German company also said it would overhaul the model strategy at its core VW division, giving a greater focus to electric and hybrid vehicles while putting only the latest and best environmental technology in diesel cars and vans.

"The Volkswagen brand is repositioning itself for the future. We are becoming more efficient, we are giving our product range and our core technologies a new focus," VW brand chief Herbert Diess said in a statement.

The company did not give details on where it would cut investments and costs.

Europe's largest carmaker is battling the biggest business crisis in its 78-year history after it admitted last month to cheating diesel emissions tests in the United States.

The scandal has wiped about a third off its market value, forced out its long-time chief executive and rocked both the global car industry and the German establishment.

Sources at the carmaker told Reuters last Friday that the VW division -- its largest by sales volume and revenue -- would likely slump to a loss this year because it was set to shoulder the bulk of the group's costs from the scandal.

Some analysts have said the group could face a bill of as much as 35 billion euros for refitting vehicles, regulatory fines, lawsuits and other costs.

At 0950 GMT, Volkswagen shares were down 1.6 percent at 106.85 euros.

($1 = 0.8795 euros)

(Reporting by Andreas Cremer; Writing by Mark Potter; Editing by Maria Sheahan and Anna Willard) ((Andreas.Cremer@thomsonreuters.com; +49-30-2888-5084; Reuters Messaging: andreas.cremer.thomsonreuters.com@reuters.net))