"Unless the hostile policy and the nuclear threat of the USA 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.
Tillerson said President Trump has always stressed on solving the nuclear testing issue of North Korea diplomatically.
The warning came from North Korea's deputy ambassador to the United Nations, Kim In Ryong, who said North Korea is now a "full-fledged nuclear power which possesses the delivery means of various ranges".
"The entire U.S. mainland is within our firing range and if the U.S. dares to invade our sacred territory even an inch it will not escape our severe punishment in any part of the globe", Mr. Kim.
The United States is not ruling out the eventual possibility of direct talks with North Korea.
US Secretary of State Rex Tillerson on Sunday asserted that his diplomatic efforts to relax tensed relations with North Korea will continue "until the first bomb drops".More news: South Park: The Fractured But Whole receives Season Pass details
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The situation on the Korean peninsula remains extremely tense.
The ministers also cut the amount of money that people can send to North Korea from $17,700 to $5,900, saying they believe the remittances are being used to back Pyongyang's arms program. Both the parties exchanged tough statements and did not exclude any option for further confrontation, including military operation.
Senior officials in President Trump's cabinet have emphasised their preference for diplomacy with North Korea, but remain prepared for the worst.
In-ryong said that this on-going threat by the USA towards North Korea meant that they had every right to possess nuclear weapons in self-defence.
"Our nuclear programs are nuclear deterrence programs aimed at protecting our independence; we have no choice but to develop our nuclear programs", he said, according to Russian state news agency Tass.