Apple CEO Tim Cook says he'll fight the US government over a demand to build a backdoor in the iPhone

Apple CEO Tim Cook has criticised the FBI after it called on Apple to break into the iPhone of a shooter in San Bernardino, California.

Cook published an open letter to Apple's customers on Wednesday attacking the US government, which wants Apple to break into an iPhone 5C belonging to Syed Farook, one of the shooters involved in last December's mass shooting attack.

Specifically, the FBI wants Apple to remove the limit on the number of times the passcode can be tried. It also wants Apple to modify its iOS operating system so passcodes can be input electronically.

Apple argues this amounts to a backdoor it would have to write, which would later be open to abuse.

"The government suggests this tool could only be used once, on one phone," the letter on Apple.com reads. "But that's simply not true. Once created, the technique could be used over and over again, on any number of devices. In the physical world, it would be the equivalent of a master key, capable of opening hundreds of millions of locks - from restaurants and banks to stores and homes. No reasonable person would find that acceptable."

The letter comes a day after US magistrate Sheri Pym ordered Apple to hack into the phone.

Cook argues that complying with the order would have "implications far beyond the legal case at hand," adding that it undermines users' privacy.

"The government is asking Apple to hack our own users and undermine decades of security advancements that protect our customers," writes Cook. "We can find no precedent for an American company being forced to expose its customers to a greater risk of attack. For years, cryptologists and national security experts have been warning against weakening encryption. Doing so would hurt only the well-meaning and law-abiding citizens who rely on companies like Apple to protect their data."

There's an ongoing debate about the use of encryption by tech companies. Some politicians and law enforcement officials fear that the use of encryption that cannot be cracked by anyone - even the tech companies themselves or law enforcement with a warrant - means that vital evidence for criminal investigations is "going dark."

Technologists and security experts counter that encryption is also used to protect vital financial, business and government data, and any attempt to weaken it will leave ordinary people more at risk from criminal and government hackers.

Last year, the White House said it wasn't going to try and ban encryption - but it didn't rule out a potential ban in the future altogether.