The iPod-owner's filing with the US Patent and Trademark Office said that the New York logo will cause "consumer confusion resulting in damage and injury" to Apple, and will "cause dilution of the distinctiveness" of Apple's trademark.
The new 'Big Apple' morphs the symbol for infinity, similar to a figure eight on its side, with the outline of an apple, featuring a stalk and leaf.
New York's official travel and tourism organisation, NYC & Company, filed the trademark application in May last year and began using the logo across print, TV, the internet and on taxis and bus shelters as part of a campaign urging New Yorkers to reduce their pollution and greenhouse gases.
Apple challenged the application in January, but last month New York protested Apple's challenge, saying its protection of the logo is too broad.
An NYC & Company spokeswoman, said: "We believe the 'infinity apple' design and its mission to create environmental awareness are unique and distinctive and do not infringe upon the Apple computer brand."
The case has echoes of Apple's long-running legal battles with the Beatles and its Apple Corps record label. The two wrangled about the usage of the name Apple and its associated logos, ending a long-term trademark dispute in February 2007.