The library received the stories, titled "The Crystal Balls" and "The Flies," as part of a private donation of the magazine's archives in 2007, library spokesman Hakan Farje said.
Larsson never had time to enjoy the success of his Millennium trilogy of crime novels, which have sold more than 20 million copies worldwide. He died in 2004 of a heart attack at age 50, a year before the first novel in the series, "The Girl With the Dragon Tattoo," was published in his native Sweden.
In the letter to the Jules Verne magazine, Larsson described himself as "a 17-year old guy from Umea with dreams of becoming an author and journalist," Farje said. He called the science fiction stories his "first tentative efforts" at writing.
Farje said the author's heirs should decide whether to publish the stories.
Larsson had originally planned to compose 10 books in the Millennium series and had written about half of a fourth book before he died. That work hasn't been published because of a legal battle over Larsson's estate between his brother and father and Larsson's longtime partner, Eva Gabrielsson.
Public access to material in the archive of the Swedish National Library is decided on a case-by-case basis, depending on the content. Farje said it was unclear if the public will get access to Larsson's work.