Cook was speaking at an Apple product unveiling at the company's headquarters, one day before a court hearing on a hotly contested FBI effort to force the company to help break into the iPhone of a shooter involved in a deadly December attack.
"We need to decide as a nation how much power the government should have over our data and our privacy," Cook told the crowd gathered for the event.
Cook's remarks were the latest in a battle with the US government over efforts to compel Apple to help the FBI break into the iPhone of one of the attackers in last year's deadly shooting rampage in San Bernardino, California.
Apple, backed by a broad coalition of technology giants like Google, Facebook and Yahoo, argues that the FBI is seeking a "back door" into all iPhones as part of the probe into the December 2 massacre that left 14 people dead.
The US Justice Department argues that it is making a "modest" demand that could help reveal vital evidence in a terror case.
An FBI victory could serve as a legal precedent backing requests for access to iPhones by law enforcement agencies throughout the United States.