Donald Trump has previously said that "North Korea best not make any more threats to the United States".
North Korea has criticized a series of deployment of USA strategic military assets to the Korean Peninsula, calling it a "death cry".
Mr Kim warned that tensions on the peninsula have "reached the touch-and-go point and a nuclear war may break out any moment".
On Saturday he also singled out North Korea's development of deliverable nuclear weapons as "the most significant geopolitical risk" to otherwise steady growth in the global economy.
North Korea also called on the United States to stop its hostile policy in regards to Pyongyang, following Pyongyang's recent statements at the 137th Inter-Parliamentary Union Assembly in St. Petersburg.
"Unless the hostile policy and the nuclear threat of the United States is thoroughly eradicated, we will never put our nuclear weapons and ballistic rockets on the negotiation table under any circumstance", Kim In Ryong told UN General Assembly's committee on disarmament.
"They stressed once again that they consider possession of nuclear weapons as the only effective way to protect their country and their people and the only guarantee of their sovereignty".
"The entire USA mainland is within our firing range and if the US dares to invade our sacred territory even an inch it will not escape our severe punishment in any part of the globe", he said.
North Korea's deputy United Nations ambassador called his country's nuclear and missile arsenal "a precious strategic asset that can not be reversed or bartered for anything".
In-ryong said that this on-going threat by the U.S. towards North Korea meant that they had every right to possess nuclear weapons in self-defence.
The tension between the two nuclear power countries has intensified as North Korea continues to develop and threaten the use of its nuclear weapons.