United States President Donald Trump has boasted that his "nuclear button" is "much bigger and more powerful" than Kim Jong-un's, in comments likely to fuel further tensions with the North Korean leader.
The outburst came in response to Mr Kim's New Year address, in which he said all of the US was within range of his country's nuclear missiles and also offered to hold talks with South Korea.
In a speech broadcast on state TV, the North Korean leader said: "The US cannot declare war against us. The entire US territories are within our firing range and the nuclear missile button is right there on my desk.
"We have secured powerful deterrence against the nuclear threat from the US."
In an earlier tweet, Mr Trump said the US-led campaign of sanctions and "other pressures" was beginning to have a "big impact" on North Korea.
He referred to the recent, dramatic escape of at least two North Korean soldiers across the heavily militarised border into South Korea.
"Soldiers are dangerously fleeing to South Korea. Rocket man now wants to talk to South Korea for first time," Mr Trump said.
"Perhaps that is good news, perhaps not — we will see!"
In response to Mr Kim's overture, South Korea offered high-level talks on January 9 at the shared border village of Panmunjom to discuss Winter Olympic cooperation and how to improve overall ties.
North Korea did not immediately react to the South's proposal. If there are talks, they would be the first formal dialogue between the two nations since December 2015.
Does Trump really have a button?
While Mr Trump's tweet may have ratcheted up the tension, he does not actually have a physical nuclear button.
The process for launching a nuclear strike is secret and complex, though some details are known.
It involves the use of a nuclear "football", which is carried by a rotating group of military officers everywhere the President goes and is equipped with communication tools and a book with prepared war plans.
If the President were to order a strike, he would identify himself to military officials at the Pentagon with codes unique to him.
Those codes are recorded on a card known as the "biscuit" that is carried by the President at all times.
He would then transmit the launch order to the Pentagon and Strategic Command.
Trump announces 'fake news media awards'
In a second tweet posted on Wednesday, Mr Trump said he would announce awards next week for "the most dishonest and corrupt media".
Mr Trump and his supporters have adopted the term "Fake News" to describe critical media coverage of his presidency.
He has been particularly scathing of reports by The New York Times, The Washington Post and CNN.