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The book was initially produced last year in an edition of seven handwritten copies. Six were given away by Rowling as gifts, and one was bought by Internet retailer Amazon at an auction for almost 2 million pounds ($3 million).
Rowling told the schoolchildren at the launch that she published the book after complaints from readers over the sale.
"There was quite a lot of high feeling from Harry Potter fans that only someone who had 2 million pounds could afford to read the book," she said. "I thought: 'fair point,' so I thought I'll publish it and then the charity can have that money too."
Rowling read a passage from the tales to her young audience, which was given free copies of book.
Amazon is printing 100,000 copies of a leather-bound collectors' edition priced at 50 pounds, or $100 in the United States.
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