According to KCNA, the proposed tests are the result of years of development and "diligent research" into heat-resistant materials and technology.
Kim Jong Un guided an "environmental simulation for re-entry by the warhead tip," the report said.
South Korean President, Park Geun-Hye, warned North Korea should be ready to accept the consequences if it did not curb its nuclear ambitions.
"North Korea will walk the path of self-destruction if it does not change," Park said at a cabinet meeting.
South Korea's Defense Ministry spokesman, Moon Sang-kyun, also questioned the authenticity of the claims.
"It's North Korea's one-way statement. From our analysis on various sources, it has not achieved re-entry technology," he said at a press briefing.
How serious are these threats?
This KCNA report is the latest in a string of combative statements and actions from the North Korean regime in recent weeks.
Last Thursday, North Korea fired two short-range ballistic missiles
toward the sea.
On Saturday, the United States and South Korea began an eight-week series of annual joint military exercises billed as the largest ever
North Korea said last week that it would make a "pre-emptive and offensive nuclear strike" in response to the exercises.
"Every year these exercises get North Korea a little excited," Daniel Pinkston, Former North East Asia Senior Analyst at International Crisis Group, told CNN.
"There are a few things going on that are driving this" in addition to the exercises, he said.
"The North Korean Party Workers' congress is coming up in May, so there's enthusiasm to present successes before then."
Pyongyang's true capacity in this area remains something of a mystery.
"They have an incentive to exaggerate their capabilities -- particularly for their domestic audience -- to demonstrate awe and power, but we don't know the exact capabilities," said Pinkston.
'We know they have conducted four tests, so they have a lot of data," says Pinkston. "We also know this is important to them and they allocate a lot of resources to it."
He added that a particular concern is that an accident could spark disaster amid heightened tensions.
"In times of crisis there could be a misperception, or a misreading of the situation, and the weapon could be used and that would be catastrophic. So that is quite worrisome."
A KCNA report earlier this month said North Korea claims to have miniaturized nuclear warheads to fit on ballistic missiles
The agency published photographs that appeared to show Kim visiting a facility where the warheads had been made to fit on ballistic missiles -- the first time state media has released images showing its purported miniaturized weapons technology.
CNN cannot independently confirm the photos' veracity or the claims of the KCNA.