North Korean leader Kim Jong-Un warned the United States Monday 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 Monday.

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

- 'Make a breakthrough' -

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 Monday 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.

The North and the South should "depart from the past, improve relations and take decisive measures to make a breakthrough in efforts to achieve reunification", he said.

South Korea's presidential Blue House welcomed the dialogue offer.

"Should the Olympics be staged succesfully, it will contribute to peace not only on the Korean peninsula but in the region and the world as well," it said in a statement.

Some analysts said Kim may be trying indirectly to lower the temperature with Washington.

At a time when the risk of a US pre-emptive strike is "higher than ever", Koh Yu-Hwan, political science professor at Dongguk University, said the speech indicated Kim was using the Olympics gesture to "shift from confrontation to peaceful coexistence with the United States".

"When he said a nuclear launch button is always on his desk, he is hinting it is not necessary for the North to stage nuclear or ICBM tests in the foreseeable future," Koh told AFP, adding however that Kim also wanted to build "massive nuclear retaliation capabilities".

Professor Yang Moo-Jin of the University of North Korean Studies in Seoul said Kim "is extending an olive branch toward the South as the US is expected to keep up with pressure and sanctions on the country throughout this year... as a whole the emphasis is on peace rather than confrontation".

In December the United Nations Security Council unanimously passed new, US-drafted sanctions against Pyongyang, restricting oil supplies vital for the impoverished state.

The most recent set of sanctions, which the North slammed as an "act of war", also received the backing of China -- the country's sole major ally and economic lifeline.

Observers say Washington must open talks with the North to defuse tensions but that remains a challenge.

Pyongyang has always said it will only deal with the US from a position of equality as a nuclear state. Washington has long insisted that it will not accept a nuclear-armed North.