A federal district judge has denied Apple’s attempt to get a preliminary injunction against Amazon’s use of the phrase “app store” for its developer program.

Judge Phyllis Hamilton for the U.S. District Court in Oakland, Calif., ruled yesterday that Apple “has not established a likelihood of confusion” and rejected the company’s bid to force Amazon to stop using the phrase, but stopped short of ruling that “App Store” was too generic to merit a trademark, as Amazon claims.

“The court finds that Apple has not established likelihood of success as to the

infringement claims,” Hamilton wrote in her decision. “The court assumes without deciding that the ‘App Store’ mark is protectable as a descriptive mark that has arguably acquired secondary meaning. The court does not agree with Amazon that the mark is purely generic, for the reasons argued by Apple, but also does not find that Apple has shown that the mark is suggestive, as there appears to be no need for a leap of imagination to understand what the term means.”

Apple, which applied for a trademark on the phrase “App Store,” sued Amazon in March after the online retail giant launched its Android application storefront, dubbed Amazon Appstore for Android.

Hamilton’s ruling on the injunction did not seem to bode well for Apple’s case. The judge ruled that Apple “has not established that it is likely to prevail on the ‘confusion’ element of its infringement claim” and found that just two of Apple’s eight arguments “somewhat favor” the company’s trademark claim. Hamilton also ruled that “three factors somewhat favor Amazon.  The remaining three factors are neutral, or do not clearly favor either side.”

Apple is fighting to protect the App Store mark on several fronts. Microsoft, Nokia, Sony Ericsson and HTC are all contesting the validity of the term as a trademark in Europe, arguing that “app store” cannot be registered as a trademark because it is generic. Microsoft has also filed an opposition to the trademark application with the U.S. Patent Office.