North Korea said that “reckless remarks” by Pompeo made it clear that Washington has no intention of resuming nuclear talks.
Tokyo's defense ministry said the projectiles fell short of Japanese waters.
The latest correspondence came as Kim observed the firing of tactical guided weapons.
South Korea condemned the launches as "extremely inappropriate given the difficult situation the world is experiencing."
North Korea hasn't reported any cases of the coronavirus, formally known as COVID-19, which has spread worldwide.
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.
North Korea reported its drills two days after the U.S. and South Korea postponed joint exercises due to coronavirus fears.