North Korean leader Kim Jong-Un yesterday warned the United States he has a "nuclear button" on his table but offered an apparent olive branch to South Korea in a New Year message, saying he was prepared for talks and may send a team to the Winter Olympics there.

Kim struck a generally defiant note after a year of rising tensions marked by the North's multiple missile launches and its sixth and most powerful nuclear test -- purportedly of a hydrogen bomb.

"We must mass-produce nuclear warheads and ballistic missiles and speed up their deployment," he said in his annual televised address to the nation.

He reiterated his claim that his country had achieved its goal of becoming a nuclear state but insisted the expansion of the weapons programme was a defensive measure.

"We should always keep readiness to take immediate nuclear counter-attacks against the enemy's scheme for a nuclear war."

The North claims it needs nuclear weapons to protect itself from a hostile Washington and has striven to create a warhead capable of targeting the US mainland with an atomic warhead.

US President Donald Trump has responded to each test with his own amplified declarations, threatening to "totally destroy" Pyongyang and taunting Kim, saying he was on "a suicide mission".

But far from persuading Kim to give up his nuclear drive, analysts say Trump's tough talk may have prompted the North Korean leader to push through with his dangerous quest.

"(The North) can cope with any kind of nuclear threats from the US and has a strong nuclear deterrence that is able to prevent the US from playing with fire," Kim said yesterday.

"The nuclear button is always on my table. The US must realise this is not blackmail but reality."

When asked for a response to Kim's claim that he had a nuclear button on his desk, Trump said "We'll see, we'll see", in comments to reporters during the New Year's Eve party at his Mar-a-Lago resort in Florida.

Kim also sugared his speech with a conciliatory tone towards Seoul, indicating for the first time that the North is considering taking part in the South's Winter Olympics next month.

"(The Olympics) will serve as a good chance to display our Korean people's grace toward the world and we sincerely hope the Games will be a success," he said.