The ultimatum came after Russian publishing house Eksmo brought out the second in a series of children's novels by Russian author Dmitri Yemets featuring a character called Tanya Grotter.
The rivals
Yemets, whose novels feature magical adventures similar to those which made Harry Potter a household name all over the world, denies stealing ideas and describes his work as a "cultural reply" to the more famous British series.
Now a Western law firm, LeBoeuf, Lamb, Green and MacRae, has written to his publisher demanding an end to publication.
"These books were translated into English, they were compared with Harry Potter books and it was determined that they are a plagiarism," Natalya Dolgova, a spokeswoman for Rowling's own Russian publisher Rosman, told the French news agency AFP.
"Dmitri Yemets has stolen Rowling's idea and she is very displeased about it."
Warner Brothers, which has purchased film, merchandising and other rights to Harry Potter novels, is backing the legal action.
The second Harry Potter film has just had its world première.
'Serious competitor'
Yemets told BBC News Online in an interview in September that his books - were "based on Russian culture and traditions".
The first novel, Tanya Grotter and Her Magic Double Bass, sold 100,000 copies and Tanya Grotter and the Disappearing Floor came out last week. The author plans further novels in the series.
He was defended by a spokesman for Eksmo, Alexei Shekhov, who said it would continue publishing the Grotter books regardless.
"We will publish them regardless of this stupid pressure," he said, adding that the Western novelist's lawyers had "got worried about a serious competitor".