Exclusive: Tim Cook Not Budging on Apple Privacy Decision: 'Safety of the Public Is Incredibly Important'

He told ABC News' David Muir why he would not break into Syed Farook's iPhone.

"I think safety of the public is incredibly important -- safety of our kids, safety of our family is very important," Cook said. "The protection of people's data is incredibly important, and so the trade-off here is we know that doing this could expose people to incredible vulnerabilities."

The interview will air today on "World News Tonight with David Muir" at 6:30 p.m. ET and on "Nightline" at 12:35 a.m. The extended interview will be available online at ABCNews.com immediately after "World News Tonight."

"This [master key] is not something we would create," Cook said. "This would be bad for America. It would also set a precedent that I believe many people in America would be offended by."