"North Korean Leader Kim Jong Un just stated that the 'Nuclear Button is on his desk at all times,' he wrote on Twitter. "Will someone from his depleted and food starved regime please inform him that I too have a Nuclear Button, but it is a much bigger & more powerful one than his, and my Button works!"

During his New Year's address, Kim reportedly claimed he has a nuclear button on his desk and said "the whole territory of the U.S. is within the range of our nuclear strike".

"This is just a reality, not a threat," he said in the televised address, according to the South's Yonhap News Agency.

Earlier Tuesday, Nikki Haley, the U.S.'s UN envoy, told reporters the U.S. "will never accept a nuclear North Korea" amid reports indicating Pyongyang is readying a new ballistic missile test.

"I hope that does not happen. But if it does, we must bring even more measures to bear on the North Korean regime," she said. "The civilized world must remain united and vigilant against the rogue state's development of a nuclear arsenal."

During his New Year’s address, Kim also offered to send a delegation to the 2018 Winter Olympics in the South in February.

South Korean President Moon Jae-in called for his government to “quickly” act on the offer of dialogue. But Haley threw cold water on the notion that such talks could be productive without the North ending its nuclear program as a precondition for them to begin.

"North Korea can talk with anyone they want, but the U.S. is not going to recognize it or acknowledge it until they agree to ban the nuclear weapons that they have," she said.

Just hours before, Trump appeared receptive to the idea, writing on Twitter: "Rocket man now wants to talk to South Korea for first time. Perhaps that is good news, perhaps not - we will see!"

Anadolu Agency