Kim said the test confirmed "another reliable and maximum capacity to contain any nuclear threat" at a time when he needed to warn Washington and its allies that military moves against Pyongyang would lead to their "self-destruction."
"The United States and South Korea will find that they have made a terrible mistake that cannot be reversed," Pak said in a statement carried by state news agency KCNA. He had previously issued statements demanding the drills be stopped.
North Korea has condemned the drills for raising tensions and has test-fired rockets and artillery in response. South Korea and the United States say the drills are defensive, and necessary for deterring the North.
The Thursday launch was the first full ICBM test by nuclear-armed North Korea since 2017. Flight data indicated the missile flew higher and longer than any of North Korea's previous tests before crashing into the sea west of Japan.
It would be the first full-capability launch of the nuclear-armed state's largest missiles since 2017, and represents a major step in the North's development of weapons that might be able to deliver nuclear warheads anywhere in the United States.