"The only way to get information -- at least currently, the only way we know -- would be to write a piece of software that we view as sort of the equivalent of cancer. We think it's bad news to write. We would never write it. We have never written it -- and that is what is at stake here," he said. "We believe that is a very dangerous operating system."
The FBI has called on Apple to help crack into the iPhone of Syed Farook, who along with wife Tashfeen Malik killed 14 and injured 22 at a training session and holiday party in December. The FBI attempted to crack the pass code but failed because Apple phone systems have a function that automatically erases the access key and renders the phone "permanently inaccessible" after 10 failed attempts.
"If a court can ask us to write this piece of software, think about what else they could ask us to write -- maybe it's an operating system for surveillance, maybe the ability for the law enforcement to turn on the camera," Cook said. "I don't know where this stops. But I do know that this is not what should be happening in this country."
This week, FBI director James Comey urged Apple in an open letter to comply with its investigation into the massacre.
Comey wrote that the FBI wanted the chance to try to guess the pass code without the phone self-destructing and without it taking a decade to guess correctly. The FBI director said he understood the case highlights the serious tension between privacy and security. And today, CIA Director John Brennan weighed in on the side of the FBI, saying that the agency has a "legitimate basis to try to understand" what is on the San Bernardino shooter's cellphone.
Cook told ABC News today that Apple had cooperated fully with the FBI.
"We gave everything that we had," he told Muir today. "We don't know that there's any information on the phone. We don't know whether there is or there isn't. And the FBI doesn't know. ... What we do know is we passed all of the information that we have on the phone and to get additional information on it or at least what the FBI would like us to do now would expose hundreds of millions of people to issues."
Cook said that the issue was not just about privacy, but also about the public's safety.
"This case is not about one phone," Cook said today. "This case is about the future. ... If we knew a way to get the information on the phone -- that we haven't already given -- if we knew a way to do this, that would not expose hundreds of millions of other people to issues, we would obviously do it. ... Our job is to protect our customers."
ABC News' Alyssa Newcomb, Julia Jacobo, Kelly Stevenson, Mike Levine and Jim Hill contributed to this report.