Trending: PAX has lost its luster: Growth of gaming show mutes the voice of independent developers this morning released new Kindle sales stats and called this the best holiday on record for the product line — no surprise, given that it was the first shopping season for the company’s $199 Kindle Fire tablet.

The company says it sold more than 1 million Kindle devices every week in December, which would add up to more than 4 million units sold for the month. Following its traditional practice, Amazon didn’t say how the sales were distributed among various Kindle devices, which include the Kindle e-readers in addition to the new tablet.

Amazon also announced that the No. 1 and No. 4 best-selling Kindle books released in 2011 were independent works published electronically through the Kindle Direct Publishing program, not from a traditional publishing house. “The Mill River Recluse,” by Darcie Chan was the top Kindle title, and “The Abbey,” by Chris Culver was fourth.

In a news release, Amazon CEO Jeff Bezos called it “a huge milestone for independent publishing.”

It’s also a key milestone for Amazon as it seeks more influence over pricing and distribution of electronic books, to support initiatives such as its Kindle Owners’ Lending Library program, which gives Amazon Prime subscribers access to one book a month as part of their $79/year subscription fee. The biggest book publishers aren’t supporting it.

Among other stats, Amazon says gifting of Kindle books rose 175 percent for the holiday shopping season (from Black Friday to Christmas Day) compared to the same period last year. In addition, Christmas Day set a new record for the most Kindle book downloads in a single day, as people unwrapped their new devices and tried them out.

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