In court papers Apple says law enforcement authorities are seeking "dangerous powers" and the move violates its constitutional rights.
The FBI and White House have said the request is limited to one iPhone.
But Apple says the software needed to comply with the FBI's request "simply does not exist".
Instead Apple says it would have to create a new version on the iPhone operating software, containing a back door to the device's encrypted data.
Meanwhile, Apple supporters protested over government efforts to break into the iPhone.
(BBC News)
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