A public letter
, signed by Apple CEO Tim Cook and published Tuesday, warns that complying with the order would entail building "a backdoor to the iPhone" -- "something we consider too dangerous to create."
"The government is asking Apple to hack our own users and undermine decades of security advancements that protect our customers -- including tens of millions of American citizens -- from sophisticated hackers and cybercriminals," the letter said.
Such a move would be an "unprecedented step," threatening the security of Apple's customers, it said.
"No reasonable person would find that acceptable."
The letter called for a public discussion on the order, saying the company was "challenging the FBI's demands with the deepest respect for American democracy and a love of our country."
"We believe it would be in the best interest of everyone to step back and consider the implications," the letter said.
Passcode thwarts investigators
A judge in California ordered Apple on Tuesday to help the FBI break into the phone of San Bernardino shooter Syed Farook.
Farook and his wife, Tashfeen Malik
, killed 14 people in the December shooting. The couple, radical Islamists who supported ISIS
, later died in a shootout with police.
Investigators had obtained permission to retrieve data from the phone but had been unable to search the device as it had been locked with a user-generated numeric passcode.
Apple's operating systems included an auto-erase function that, when enabled, would result in the information on the phone being permanently wiped after 10 failed attempts at inputting the passcode, the government wrote in documents seeking the order.
"We have made a solemn commitment to the victims and their families that we will leave no stone unturned as we gather as much information and evidence as possible. These victims and families deserve nothing less," Eileen Decker, U.S. attorney for the Central District of California, said in a statement in response to the court order.
"The application filed today in federal court is another step -- a potentially important step -- in the process of learning everything we possibly can about the attack in San Bernardino."
The point was echoed Wednesday in a Justice Department statement that stressed, from its perspective, what the judge's order does and does not do.
"It is unfortunate that Apple continues to refuse to assist the department in obtaining access to the phone of one of the terrorists involved in a major terror attack on U.S. soil," it read.
"The judge's order and our request in this case do not require Apple to redesign its products, to disable encryption or to open content on the phone. In addition, the judge's order and our request were narrowly tailored to this particular phone," the statement said.
Apple said the FBI had requested that the tech giant produce a new version of the iPhone operating system that circumvented key security features to install on Farook's phone.
"In the wrong hands, this software -- which does not exist today -- would have the potential to unlock any iPhone in someone's physical possession," Cook's letter said.
The FBI did not describe such a move as a "backdoor" into the iPhone, but complying with the request would "undeniably" create one, and limiting its use to the Farook case could not be guaranteed, the letter said.
"The government suggests this tool could only be used once, on one phone. But that's simply not true. Once created, the technique could be used over and over again, on any number of devices," it said.
"The same engineers who built strong encryption into the iPhone to protect our users would, ironically, be ordered to weaken those protections and make our users less safe," the letter continued, adding it could find "no precedent for an American company being forced to expose its customers to a greater risk of attack."
Apple: Implications 'chilling'
Apple, which has helped the FBI with similar requests in the past, said in the letter that it had "great respect for the professionals at the FBI, and we believe their intentions are good."
"We have no sympathy for terrorists," it said, adding it did not oppose the order lightly.
But it said the FBI was proposing "an unprecedented use" of law dating from 1789 to justify an expansion of its authority, the implications of which were "chilling."
"If the government can use the All Writs Act to make it easier to unlock your iPhone, it would have the power to reach into anyone's device to capture their data," it said.
"The government could extend this breach of privacy and demand that Apple build surveillance software to intercept your messages, access your health records or financial data, track your location, or even access your phone's microphone or camera without your knowledge."
Republican presidential candidate Donald Trump gave his take on the standoff Wednesday, saying Apple should comply with the judge's order.
"I agree 100% with the courts," Trump said on "Fox and Friends."
"I think security over all -- we have to open it up, and we have to use our heads."