North Korea's Kim Jong-un "will be tested like never before," US President Donald Trump said as the two leaders continued to trade insults and Pyongyang threatened to test a hydrogen bomb over the Pacific Ocean.

Mr Kim called Mr Trump "mentally deranged" and vowed to make him pay dearly for threatening to destroy his country hours after the US imposed fresh sanctions over Pyongyang's weapons programmes.

Mr Trump issued his response on Twitter.

Kim Jong Un of North Korea, who is obviously a madman who doesn't mind starving or killing his people, will be tested like never before! — Donald J. Trump (@realDonaldTrump) September 22, 2017

Tensions have risen as North Korea has resisted intense international pressure to halt its nuclear and missile programmes, with Mr Trump and Mr Kim exchanging ever-more threatening rhetoric.

The US president said in his first address to the United Nations on Tuesday he would "totally destroy" the country of 26 million people if the North threatened the United States and its allies, and called Kim a "rocket man" on a "suicide mission".

Mr Kim said the North would consider the "highest level of hard-line countermeasure in history" against the United States and that Mr Trump's comments had confirmed his nuclear programme was "the correct path".

Pyongyang conducted its sixth and largest nuclear test on 3 September and has launched dozens of missiles this year as it accelerates a programme aimed at enabling it to target the United States with a nuclear-tipped missile.

Mr Kim said Mr Trump would face "results beyond his expectation", without specifying what action North Korea would take next.

"I will surely and definitely tame the mentally deranged US dotard with fire," Mr Kim said in the rare direct statement carried by the KCNA state news agency, referring to Mr Trump.

North Korean Foreign Minister Ri Yong Ho was asked what Mr Kim might do and said Pyongyang could consider a hydrogen bomb test on the Pacific Ocean of an unprecedented scale, South Korea's Yonhap news agency reported.

Mr Ri, who was talking to reporters in New York, however said he did not know Mr Kim's exact thoughts, according to the report.

The escalating rhetoric came even as UN Secretary-General Antonio Guterres called for statesmanship to avoid "sleepwalking" into a war.

South Korea, Russia and China all urged calm.

However, the rhetoric was starting to rattle some in the international community. French Sports Minister Laura Flessel said France's team would not travel to the 2018 Winter Olympic Games in South Korea if its security cannot be guaranteed.

The 2018 Games are to be staged in Pyeongchang, just 80km from the demilitarised zone between North and South Korea, the world's most heavily armed border.

In his sanctions announcement yesterday, Mr Trump stopped short of going after Pyongyang's biggest trading partner, China, praising as "tremendous" a move by its central bank ordering Chinese banks to stop doing business with North Korea.

The additional sanctions on Pyongyang, including on its shipping and trade networks, showed that Mr Trump was giving more time for economic pressures to weigh on North Korea after warning about the possibility of military action on Tuesday.

Asked ahead of a lunch meeting with the leaders of Japan and South Korea if diplomacy was still possible, Mr Trump nodded and said: "Why not?"

He said the new executive order on sanctions gives further authority to target individual companies and institutions that finance and facilitate trade with North Korea.

It "will cut off sources of revenue that fund North Korea's efforts to develop the deadliest weapons known to humankind", Mr Trump said.

The US Treasury Department now had authority to target those that conduct "significant trade in goods, services or technology with North Korea".

US Treasury Secretary Steven Mnuchin said banks doing business in North Korea would not be allowed to also operate in the United States.