The President has already deployed a US Navy aircraft carrier into the Sea of Japan, but said that “powerful submarines” will follow in its path.
North Korea has threatened that it will retaliate “by powerful force of arms”, and has said that it is “ready to react to any mode of war desired by the US”.
While the world’s eyes are fixed on Kim, his wife Ri Sol-ju remains elusive. Very little is known about the North Korean First Lady, who is thought to be in her late 20s.
She was first pictured accompanying her husband to an event in summer 2012, and in July North Korean state media confirmed that they were married.
It is thought that the wedding took place in 2009 as Kim prepared to succeed his father Kim Jong-il.
Kim Jong-un reportedly married Ri Sol-ju in 2009
Ms Ri is thought to be in her late 20s
Ms Ri was formerly a member of the Unhasu Orchest
“The late North Korean leader Kim Jong-il arranged his youngest son's marriage in a hurry after suffering a stroke in 2008,” analyst Cheong Seong-chang said.
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There have been reports that Kim welcomed a baby in 2010, but it is unknown whether Ms Ri is the child’s mother.
“Ri Sol-ju performed on stage in 2010 as a member of the Unhasu Orchestra, when Kim Jong-un became the father of his first child," the South Korean Chosun Ilbo newspaper quoted a diplomatic source in Beijing as saying.
“In North Korea, it is unthinkable for a pregnant first lady to perform on stage.”
The Kim Dynasty: Inside North Korea's secretive 'first family'
Tue, February 14, 2017
The fate of the ruling Kim's family of North Korea, the world's only hereditary totalitarian Stalinist state.
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KIM JONG-SUK: North Korean founder Kim Il-sung and his first wife Kim Jong-suk gave birth to their son Kim Jong-il in 1941.
Ms Ri looked heavily pregnant when she attended a memorial for Kim Jong-il
Dennis Rodman revealed that Ms Ri gave birth to a daughter in 2013
In December 2012, Ms Ri appeared to be sporting a large baby bump as she attended a memorial to Kim Jong-il.
Months later Kim’s friend, the former-basketball player Dennis Rodman, revealed that she had recently given birth to a baby daughter named Ju-ae.
There was speculation last year that Ms Ri had fallen out of favour with the Kim family after she was not seen in public for nine months.
Some suggested that she might have had a disagreement with her husband’s sister Kim Yo-jong, who is responsible for establishing Jong-un’s cult of personality.
Fears that Ms Ri might have been executed were assuaged in December, when she was pictured attending an air combat training competition with her husband.