Speaking to the Telegraph during a tour of Europe and Israel, Cook said that the public should not accept "the government or a company or anybody" having access to private information.
"This is a basic human right. We all have a right to privacy. We shouldn't give it up. We shouldn't give in to scare-mongering or to people who fundamentally don't understand the details," he continued.
"History has taught us that privacy breaches have resulted in dire consequences. You don't have to look back too far or be a historian to see these things. They are readily apparent."
Of whether or not accessing personal information would help fight terrorism Cook said the encryption tools used by terrorist groups would mean the only people affected by a crack down would be "good people".
"Terrorists will encrypt. They know what to do. If we don't encrypt, the people we affect are the good people.
You don't want to eliminate everyone's privacy. If you do, you not only don't solve the terrorist issue but you take away something that is a human right. The consequences of doing that are very significant."
In addition to governments Cook added big companies should not have unlimited access to consumer data.
"If you want to keep your health personal, you shouldn't have to share it with your insurance company.
These things are not meant to be on some bulletin board somewhere."
The Apple boss added the company had a "very straightforward business model".
"We design our products such that we keep a very minimal level of information on our customers," he added.
"We don't make money selling your information to somebody else. We don't think you want that.
We don't want to do that. It's not in our values system to do that.
"We are not a treasure trove of data. It is a cop out to say: choose between privacy or security.
There is no reason why customers should have to select one. There is no reason not to have both."