CUPERTINO, CA — (CNN) Apple has responded to a California judge’s order to help the FBI break into the phone of one of the San Bernardino shooters with a public letter saying it opposes such a move, labeling the instruction “an overreach by the U.S. government.”

The letter, signed by Apple’s CEO Tim Cook and published Tuesday, warns that complying with the order would entail building “a backdoor to the iPhone,” creating “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 reads.

Such a move would potentially render tens of millions of devices vulnerable.

“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 read.

A judge in California ordered Apple on Tuesday to help the FBI break into the phone of Syed Farook, one of the San Bernardino shooters.

Farook, along with his wife, killed 14 people in San Bernardino, California, in December. The couple was later killed in a shootout with police.

Authorities had obtained permission to retrieve data from the device.

However, investigators 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 device becoming permanently inaccessible 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.”

Apple said that the FBI had requested that the tech giant produce a new version of the iPhone operating system which 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.

While the FBI did not describe this as a backdoor into the iPhone, complying with the request would “undeniably” create one, and limiting its use to the Farook case could not be guaranteed, it 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, 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 that it did not oppose the order lightly.

But it said that 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.”

The-CNN-Wire ™ & © 2016 Cable News Network, Inc., a Time Warner Company. All rights reserved. (PHOTO: Jeff King/CNN)