The FBI’s claims that its powers of surveillance have “gone dark” are a “crock”, Apple boss Tim Cook has told Time magazine.

Cook is currently embroiled in an escalating war of words with the US authorities over Apple’s refusal to break into the iPhone of San Bernardino terrorist Syed Farook.

The FBI has accused Apple of posturing as “the primary guardian of Americans’ privacy” and putting its brand ahead of public safety. Apple has responded by accusing the FBI of deliberately intending to smear the company and “throwing decorum to the winds”.

US authorities have long been concerned about the increasing use of encryption – the basis of digital security – by tech companies. Last year the FBI director, James Comey, warned increasing encryption threatened to take the world to a “very, very dark place”, leaving law enforcement unable to access information.

“Going dark – this is a crock,” Cook told Time. “No one’s going dark. I mean really, it’s fair to say that if you send me a message and it’s encrypted, they can’t get that without going to you or to me, unless one of us has it in our cloud at this point. But we shouldn’t all be fixated just on what’s not available. We should take a step back and look at the total that’s available, because there’s a mountain of information about us.”

In the interview Cook’s dismisses the FBI’s argument that only one iPhone will be affected by the Farook case. Creating a “back door” into Farook’s iPhone “puts millions of people at risk”. Such software could be used by criminals and other bad actors to crack into anyone’s iPhone, Apple has argued. “It’s not about one phone,” Cook told Time. “It’s very much about the future.”

Cook also poured cold water on Comey’s arguments that Apple’s encryption technology has left law enforcement unable to access the data of terrorists, pedophiles and other bad actors.

If there was a ban or a weakening placed on Apple’s encryption then “I would argue that the bad guys will use encryption from non-American companies, because they’re pretty smart, and Apple doesn’t own encryption”, said Cook.

“The internet doesn’t have boundaries,” he said. “You can wind up getting an app from eastern Europe or Russia or wherever, it doesn’t matter which country, just outside the United States. And that app would give you end-to-end encryption.”