South Korea will arm itself with nuclear weapons if its rogue neighbour, North Korea, continues to develop the bomb

This would be a revolutionary step, overturning half a century of opposition to nuclear capability. South Korea has committed to the Nuclear Non-Proliferation Treaty.

"It will become a domino effect and even South Korea will become concerned and develop nuclear weapons, and maybe Japan as well," according to a senior official in the Seoul government.

"This will all lead to a big security threat," the director-general for reunification policy in the Ministry of Unification, Lee Duk-haeng, told Fairfax Media.

"This is no longer an issue within the Korean peninsula," he said, as North Korea continues to test increasingly long-range missiles.

"For Australia this is not a distant problem."

The dictatorship of Kim Jong-un conducted its fourth underground nuclear test in January in breach of UN Security Council orders.

And it continues to test ballistic missiles, most recently last Wednesday, also a breach of UN Security Council resolutions.

The regime under Kim appears to have accelerated work on developing a nuclear-tipped missile.

The policy of the South Korean government is opposed to the development of nuclear arms, but the matter is now under lively debate as North Korea persists in its illegal plans.

Like other US allies including Japan and Australia, South Korea enjoys the protection of the US nuclear arsenal, so-called extended nuclear deterrent.

But the US Republican presidential candidate Donald Trump has called this into question.

Mr Trump has said that he is prepared to walk away from the long-standing US alliances with Tokyo and Seoul unless they pay more towards the cost of the US bases on their soil.

He has also said that it might not be a bad thing for South Korea and Japan to develop the bomb, directly contradicting half a century of US non-proliferation policy.

The UN Security Council declared tough new sanctions against North Korea in March.

However, Mr Lee expressed concern that China might not be enforcing them strictly.

Beijing is Pyongyang's only ally and its dominant trading partner.

"Of course, China has been honouring its promise to conduct the UN sanctions and doing as it's supposed to do.

"But China-North Korea relations go way back and if there are areas beyond the sanctions, one concerning point is that China could be finding some way behind the scenes of supporting North Korea."

The sanctions do not apply to humanitarian aid or to materials required for daily living.

The potential to use these categories to conduct trade with the Kim regime "can be a point of concern", Mr Lee said.

An estimated 90 per cent of all North Korean trade is conducted with China, with which it shares a land border.

Mr Lee called on all regional governments, including Australia's, to take a "stern" approach to isolate North Korea over its nuclear development.

Australia has taken recent new sanctions against Pyongyang. And the acting Foreign Affairs Minister, George Brandis, this week announced that "Australia stands ready to list additional individuals and entities associated with the regime's weapons and missile technology activities".

In February, South Korea responded to the persistent North Korean nuclear development by opening discussions with the US to install an American missile interception system.

China has reacted furiously to Seoul's decision to deploy the so-called Terminal High Altitude Area Defence or THAAD.

Beijing last week began punishing South Korea by imposing undeclared trade sanctions on the country's surging cultural exports, the so-called K-Wave products, in the movie, TV, and music sectors.

Peter Hartcher Sydney Morning Herald