MILWAUKEE—Justice Brett Kavanaugh said that advancing technology would force not only a re-examination of free-speech and privacy rights, but also of war powers as international conflict expands across the internet.

“I see technology straining our traditional understandings of speech, of privacy and of war in a way that’s going to be a huge challenge for our system of separation of powers, and a huge challenge for all of us as judges and as citizens,“ he told a judicial conference here Monday night.

He...