The Korean Central News Agency said Kim guided an artillery firing competition between army units on Thursday.
KCNA said Kim showed great satisfaction as his front-line artillery units demonstrated “excellent marksmanship.”
North Korea fired three short-range projectiles off its east coast on Monday.
The launches came two days after North Korea’s state media said leader Kim Jong Un supervised an artillery drill.
Small-scale exercises with South Korea have kept U.S. troops ready for conflict with North Korea, defense officials say.
Kim has used the diplomatic stalemate to expand his military capabilities by intensifying tests of shorter-range weapons.
Kim Jong Un called for his military to prepare unspecified “offensive measures” to protect the country’s security.
The action followed reports that North Korea had warned of a possible missile launch or nuclear test for late December.
Mount Paektu and white horses are symbols associated with the Kim family's dynastic rule.
It is the latest sign of impatience from Kim amid worries that two years of U.S.-North Korean diplomacy will fall apart.