The confrontation between the technology industry and the FBI over encryption has deepened after Apple pledged to fight a court order that it help unblock an iPhone used by the perpetrators of December's San Bernardino shooting.

Tim Cook, Apple chief executive, said the federal court ruling was a "chilling" example of "over-reach by the US government" and claimed the company was being asked "to build a back door to the iPhone" that he said was "too dangerous to create".

The ruling has brought to a head a dispute over encryption and privacy between Silicon Valley and law enforcement that has been simmering for more than a year and sets up a legal showdown that could potentially end up in the Supreme Court.

Mr Cook’s sharply worded statement came hours after a judge in the US District Court in Los Angeles said the company must provide “reasonable technical assistance” to the FBI in its efforts to get information off the phone.

Industry executives fear that US government pressure to weaken encryption could damage the credibility of their products, which was already hit by the 2013 revelations from former National Security Agency contractor Edward Snowden. They also worry that authoritarian governments such as China would force them to hand over the same techniques to get around security systems.

Silicon Valley privacy campaigners have rallied to Apple’s side, but so far other large tech companies, such as Google, Microsoft and Facebook, have stayed on the sidelines.

On Wednesday, Mr Snowden tweeted his support for Apple: “This is the most important tech case in a decade. Silence means @google picked a side, but it’s not the public’s.”

Republican presidential candidate Donald Trump weighed in on the side of the courts to attack Mr Cook's stand. He told the Fox network: "Who do they think they are? They have to open it up."

The FBI has been warning for months that new encryption procedures are allowing terrorists to “go dark” from surveillance approved by courts and are making it harder to conduct investigations.

The iPhone belonged to Syed Rizwan Farook, who, alongside his wife, Tashfeen Malik, carried out a mass shooting at the San Bernardino County Department of Public Health. Mr Farook and his wife were later killed by police in a shootout.

The ruling does not ask Apple to switch off the encryption features on the phone. But it does order the company to create software to circumvent an element of the phone’s security system that erases all data on a device if the password is entered incorrectly 10 times. That would allow the FBI to use computers to try and break the password.

Prosecutors said the ruling applied only to this specific iPhone, which was owned by the government agency where Mr Farook worked. However, in theory any software developed by Apple for this case could be used on any iPhone.

Mr Cook said the US government was “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 cyber criminals”.

He said the case set a “dangerous precedent” that could lead to government demands 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”.

Mr Cook's decision to publish an open letter to customers, rather than debating the issue through the courts or in private meetings with the authorities, is unusually forthright for the company. – Copyright The Financial Times Limited 2016