Print sales for the script book have totaled 3.3 million in North America and nearly 850,000 in the U.K. since its release on July 31, according to Scholastic and Little, Brown Book Group.

Billed as the eighth Harry Potter story, the script book has also boosted sales of the original seven “Harry Potter” novels.

“Cursed Child” debuts this week at No. 1 on The Wall Street Journal’s best-seller list. “Harry Potter and the Sorcerer’s Stone,” the first book in the series, stands at No. 8. “Sorcerer’s Stone” sold 35,000 print copies in the U.S. in the week ended Aug. 7, including the original and illustrated editions, according to Nielsen BookScan data.

“The Tales of Beedle the Bard,” a spinoff book Rowling wrote for charity, rounds out the list at No. 10.

“This is way beyond our most optimistic expectations and is testament to the passion readers have for J.K. Rowling’s Wizarding World, as well as to the amazing reception the play itself has had,”David Shelley, CEO of Little, Brown Book Group said in a news release.

The play’s e-book version—published by Pottermore, Ms. Rowling’s website and publishing platform—topped Apple’s iBooks best-seller list for the week ended Aug. 7. Pottermore hasn’t released sales numbers.

Sales for “Cursed Child” still fall short of the record-breaking sales of the final novel in the original series, “Harry Potter and the Deathly Hallows,” which in 2007 sold 8.3 million copies in the U.S. in its first 24 hours. Nevertheless, Barnes & Noble and U.K. bookstore chain Waterstones both have said they expect the script book to be their biggest seller of the year. Amazon said the book was its most preordered title in print and e-book since the 2007 release of “Deathly Hallows.”

In advance of the release, Scholastic printed 4.5 million copies of the play in the U.S. and Canada. It sold more than two million copies in its first two days in North America.

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The “Cursed Child” script was written by Jack Thorne, based on a story by Rowling, John Tiffany and Thorne. The play opened in London on July 30 and is sold out through May.

A spinoff film, “Fantastic Beasts and Where to Find Them,” with ascreenplay written by Rowling, is set to debut in November. It is the first in a planned series of three “Fantastic Beasts” films.