On a visit to Edinburgh, Jeremy Hunt, the party's UK spokesman on culture, media and sport, said the extra money could have a huge impact on grassroots sport.
The Tories want lottery cash to be channelled into sport, arts, heritage and charities, reversing Labour's move to use funds for wider priorities such as health and education.
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Hide AdMr Hunt said: "We think by returning the lottery to the original four pillars and cutting administration costs and various other reforms, we could generate an extra 19m for lottery good causes in Scotland."