SEOUL—North Korea’s cyber army, long considered a midlevel security threat, is quietly morphing into one of the world’s most sophisticated and dangerous hacking machines.

Over the past 18 months, the nation’s fingerprints have appeared in an increasing number of cyberattacks, the skill level of its hackers has rapidly improved and their targets have become more worrisome, a Wall Street Journal examination of the program reveals. As recently as March, suspected North Korean hackers appear to have infiltrated Turkish banks and...