On Monday, Rogers said "strong encryption is in our nation's best interest." Asked at the conference whether he supported impenetrable encryption, Rogers replied: "That's not what I said, strong encryption is in our nation's best interests."
"Security, encryption: good. The ability to generate insights as to criminal behavior and threats to our nation's security, also good," he added.
Taking the stage before Cook, Rogers also said that a cyber-attack that hits critical infrastructure was "only a matter of when."
"It's only a matter of time I believe until someone does something destructive," Rogers said. He said he worried that the Islamic State could begin to view cyber-attacks as a "weapons system."
Both Rogers and Cook discussed how to balance privacy and state-enforced security. The NSA director acknowledged the tension between the two while emphasising threats he believed the U.S faced. Cook said there wasn't a trade-off to be made.
"Nobody should have to decide privacy and security. We should be smart enough to do both," Cook told the conference, calling any compromise a "cop-out."
"Both of these things were essential parts of our Constitution. It didn't say prioritise this one above all of these," he said. "I mean, these guys were really smart folks and they held all of these things and said all of these are what it means to be an American."
And privacy would become increasingly important to consumers over time, Cook added.
"It will become increasingly more important to more and more people over time as they realise that intimate parts of their lives are in the open and being used for all sorts of things," Cook said.