The legal response was fired in what promised to be a landmark case pitting national security against personal privacy.
Read more from our special coverage on "APPLE"
"Last week's judicial order may have prompted among the most high-profile battles we have seen over device encryption," Internet rights group Electronic Frontier Foundation said on its website.
"But this is not the first time, nor is it likely to be the last time, we are called to defend access to tools that can ensure privacy and security."
Apple chief Tim Cook has called for the stand-off to be resolved by legislation in US Congress, not in the courts.
Cook equated what the FBI was demanding as a software version of "cancer."
Apple said in a court filing that the government overstepped its legal authority in trying to force the company to facilitate access to a locked iPhone used by one of the shooters of the San Bernardino attack last year, which left 14 dead.
"No court has ever authorized what the government now seeks, no law supports such unlimited and sweeping use of the judicial process, and the constitution forbids it," Apple's lawyers wrote in the motion filed in California federal court.
The Apple response is the latest in the fight over how far the company must go in helping US law enforcement access a device with data locked by encryption that only the user can normally access.
"The government demands that Apple create a back door to defeat the encryption on the iPhone, making its users' most confidential and personal information vulnerable to hackers, identity thieves, hostile foreign agents and unwarranted government surveillance," Apple's brief said.
Apple executives, who briefed reporters on condition they not be quoted directly, said the order would effectively require the creation of a "government operating system" which could be used repeatedly by FBI forensics experts and potentially leak out to others.
The iPhone maker is arguing that the government effort violates Apple's constitutional rights to free speech, by forcing it to write software that undermines its values.
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