WASHINGTON/SEOUL (AFP, REUTERS) - US President Donald Trump on Friday (Sept 22) warned "madman" North Korean leader Kim Jong Un that he would be "tested," in the latest exchange of insults between the two.

"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!" Trump tweeted.

Earlier Friday, Kim blasted Trump as a "mentally deranged US dotard" who will "pay dearly" for threatening to destroy North Korea.

Trump "insulted me and my country in front of the eyes of the world and made the most ferocious declaration of a war in history", Kim said, according to the official Korean Central News Agency. He blasted Trump's maiden speech to the United Nations General Assembly as "unprecedented rude nonsense".

Trump had branded Kim "Rocket Man" and threatened to "totally destroy North Korea", a country of 26 million people, in his UN speech. Washington followed on Thursday by announcing tougher sanctions on North Korea.

Trump earlier threatened Pyongyang with "fire and fury." He has traded tough rhetoric with Pyongyang as it pushed an increasingly brazen weapons program in recent months, with missile launches and its sixth and largest nuclear test.

On the fringes of the UN General Assembly in New York, North Korean Foreign Minister Ri Yong Ho told reporters Pyongyang might now consider detonating a hydrogen bomb outside its territory.

Ri, however, told reporters he did not know Kim's exact thoughts.

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

"I will surely and definitely tame the mentally deranged US dotard with fire," Kim said in the statement on the KCNA state news agency.

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

Asked about the North Korean hydrogen bomb threat, Secretary of State Rex Tillerson told ABC that diplomatic efforts will continue but all military options were still on the table.

"We are quite challenged" with the escalating rhetoric, he said, but hoped increased sanctions and "voices from every corner of the world" would help lead Kim to talks.

"SLEEPWALKING INTO WAR"

In a separate report, KCNA made a rare criticism of official Chinese media, saying their comments on the North's nuclear program had damaged ties and suggested Beijing, its only major ally, had sided with Washington.

Singling out the official People's Daily and its more nationalistic sister publication, the Global Times, KCNA said Chinese media was "openly resorting to interference in the internal affairs of another country" and driving a wedge between the two countries.

At the United Nations, Secretary-General Antonio Guterres called for statesmanship to avoid "sleepwalking" into a war.

Japan, the only country ever to suffer an atomic attack, described the H-bomb threat as "totally unacceptable".

South Korea, Russia and China all urged calm. "All relevant sides should exercise restraint and dedicate themselves to easing the situation rather than irritating each other," said Lu Kang, China's foreign ministry spokesman.

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 could not 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.

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In Thursday's sanctions announcement, 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.

Asked about the order on Friday, China's foreign ministry spokesman Lu Kang said, "As far as I understand, the situation you have just mentioned does not accord with the facts. "In principle, China has always fully and strictly enforced UN resolutions and accepted our international obligations". He did not elaborate.

Chinese government ministries generally do not offer comment on decisions taken by other government departments.

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

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

Trump said the new executive order on sanctions gives further authorities 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", Trump said.

The White House said North Korea's energy, medical, mining, textiles, and transport industries were among those targeted and that the US Treasury could sanction anyone who owns, controls or operates a port of entry in North Korea.

The new measures do not target Pyongyang's oil trade.

"ON NOTICE"

US Treasury Secretary Steven Mnuchin said banks doing business in North Korea would not be allowed to operate in the United States. "Foreign financial institutions are now on notice that going forward they can choose to do business with the United States or with North Korea, but not both," Mnuchin said.

The UN Security Council has unanimously imposed nine rounds of sanctions on North Korea since 2006, the latest this month capping fuel supplies to the isolated state.

The US and South Korea are technically still at war with North Korea because the 1950-53 Korean conflict ended with a truce and not a peace treaty.

The North accuses the United States, which has 28,500 troops in South Korea, of planning to invade and regularly threatens to destroy it and its Asian allies.

On Wednesday, US Secretary of State Rex Tillerson said there were "some indications" that sanctions were beginning to cause fuel shortages in North Korea.