Barnes & Noble Inc. said that sales of digital books made through its website now exceed those of traditional books that it sells online.

Barnes & Noble, which introduced its Nook electronic reader last year to compete with Amazon.com Inc.'s Kindle, said customers bought or downloaded 1 million e-books via the Nook on Christmas Day.

A spokeswoman for Barnes & Noble said that figure included free e-books, but that most were paid downloads.

Barnes & Noble, which put itself up for sale last summer, is under pressure to show that its share of the e-books market is growing fast enough to mitigate a longstanding industry-wide decline in book sales.

Barnes & Noble says it has a 20 percent share of the e-books market.

The top U.S. bookseller also said the various versions of the Nook devices were now its best-selling product, echoing claims earlier this week by Amazon that the most recent version of the Kindle was its best-selling item ever.

Both companies do not divulge exact sales figures. The sales numbers compare the devices to items within a category, such as individual books or CDs, rather than any category as a whole.

Analysts estimate that Barnes & Noble has sold about 2 million Nooks since the device's launch, while the Kindle, launched in 2007, is thought to have sold about 6 million devices.

Barnes & Noble makes most of its book sales at its 717 namesake stores in the United States. In the quarter that ended on Oct. 30, retail location sales were more than five times greater than on its website, according to its most recent quarterly report.

Barnes & Noble shares were down 5 cents, or 0.3 percent at $14.26 in midday trading on the New York Stock Exchange.