The move marks a change in Amazon's previous position over the apparent flaw, which was to charge customers $200 to replace the device. Amazon had said the damage wasn't covered under the warranty.
Geise is asking a federal court in Seattle to make the complaint a class-action suit representing all Kindle customers affected by the alleged flaw.
Amazon Thursday refused to discuss the suit, but a spokeswoman said the retailer would replace damaged Kindles without charge.
"We do not comment on active litigation," spokeswoman Cinthia Portugal said in a statement e-mailed to InformationWeek. "Nevertheless, we encourage anyone who has an issue with the cover attachment mechanism to return the cover and device for a free replacement so we can investigate further."
However, Geise's lawyer Beth Terrell told the Seattle Times the lawsuit would go on. "If they would like to resolve the matter, I think the way to do it is through a court-approved process."
Amazon's decision to drop the $200 charge for replacing cover-damaged Kindles came after the problem was reported by many bloggers and major news companies. Amazon sells the Kindle 2 for $299 and the larger Kindle DX for $489.
Amazon launched its first Kindle in November 2007. The success of the device has been credited with proving there is a market for electronic book readers. Amazon includes with the device a free wireless connection for downloading books and magazine subscriptions from the retailer.
Amazon doesn't disclose the number of Kindles it has sold, but claims it accounts for 35% of book sales for those editions in which Kindle versions are available. Amazon's biggest rival in the e-book reader market is Sony, but Amazon could face stiff competition in the future from startup Plastic Logic, which is planning to start selling a device similar to the Kindle DX in the second half of the year.
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