Geekwire reports that Amazon regards Apple's claim to the trademark as "baseless" and even points out that Apple CEO Steve Jobs has used the term "app stores" in a generic sense.
Apple filed its complaint about Amazon's Appstore in March and has asked a federal judge in San Francisco to accelerate proceedings to enable it to impose a temporary injuction, which would force Amazon to stop using the name. The court has yet to rule on this point.
But Amazon has argued against Apple's complaint in a 10-page document, which can also be seen on the Geekwire website, countering each point made by Apple.
Amazon isn't the only company to dispute Apple's claim to the term 'App Store', with Microsoft also arguing that the term is too generic to trademark.
Earlier this week, Apple appeared to give up on its attempts to trademark the term 'pod'.