North Korea's state news agency has called the US-led effort to impose sanctions over its weapons programme futile, vowing the country inevitably will become a "state nuclear force".

The comments on Sunday came from the Korean Central News Agency's website Uriminzokkiri after US Secretary of State Rex Tillerson met for talks with China's top diplomats and President Xi Jinping in Beijing on the Korean nuclear crisis.

Tillerson has been a proponent of a campaign of "peaceful pressure", using US and UN sanctions and working with China to turn the screw on the regime.

But his efforts have been overshadowed by an extraordinary war of words, with US President Donald Trump mocking North Korean leader Kim Jong-un as "little rocket man" and Kim branding Trump a "dotard".

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"The US and the South Korean puppet forces are mistaken if they think that sanctions and pressure will keep the DPRK from attaining the goal of completing the state nuclear force," said KCNA, using the acronym for the country's official name, Democratic People's Republic of Korea.

"The US and vassal forces would be well advised to bear in mind that their frantic sanctions - contrary to the trend of the times - will lead to their final doom."

Washington has reached out to Pyongyang but received no response.

"We ask: 'Would you like talk?'" Tillerson said on Saturday. "We're not in a dark situation, a blackout. We have a couple, three channels open to Pyongyang."

In Washington, the State Department said while communications channels do exist, North Korea has shown no interest in talking about giving up its nuclear weapons.

"Despite assurances that the United States is not interested in promoting the collapse of the current regime, pursuing regime change, accelerating reunification of the peninsula or mobilising forces north of the DMZ (demilitarised zone), North Korean officials have shown no indication that they are interested in or are ready for talks regarding de-nuclearisation," spokeswoman Heather Nauert said in a statement.

The US has not ruled out the use of force to compel Pyongyang to halt missile and nuclear tests, and last week Trump threatened to "totally destroy" the country.

But privately, senior figures admit military options do not look promising, with ally South Korea's densely populated capital Seoul - a city of 25 million people - in range of North Korea's heavy artillery.

Even as Tillerson met Xi and China's top diplomats State Councillor Yang Jiechi and Foreign Minister Wang Yi, North Korea's propaganda agency fired a new barrage of insults.

A statement proclaimed Trump an "old psychopath" bent on the "suicidal act of inviting a nuclear disaster that will reduce America to a sea of flames".

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North Korea's rhetoric has been backed by a provocative series of ballistic missile tests and on September 3, it conducted its sixth and most powerful nuclear test yet.

Washington, backed by most of the international community, has declared North Korea's programme unacceptable, fearing its own vast arsenal will not deter Kim from attack.

With the world on edge, fears are growing a miscalculation from either side could trigger a renewed deadly conflict on the divided Korean Peninsula.

Some recent tests saw North Korean missiles flying over Japan en route to the Pacific, and its latest underground detonation appears to have been a powerful hydrogen bomb.

Observers have expressed concern if North Korea carries out an atmospheric nuclear test over the ocean, Washington will feel obliged to take risky military action.

But Tillerson said that decision would be up to Trump alone. "As far as I know the commander-in-chief has issued no red lines."

Tillerson instead called for calm, singling out Pyongyang's missile tests for criticism.

"The whole situation is a bit overheated right now. I think everyone would like for it to calm down," he said in response to a question about Trump's threats.

"I think if North Korea would stop firing all the missiles, that would calm down things a lot."