North Korean leader Kim Jong-un has reacted angrily to President Trump's speech at the United Nations General Assembly, calling it "unprecedented rude nonsense".

The North Korean leader said he will make the US President "pay dearly for his speech calling for totally destroying" North Korea.

"I am now thinking hard about what response he could have expected when he allowed such eccentric words to trip off his tongue," Kim said in a statement released by the state Korean Central News Agency, which also published a photo of the North Korean leader sitting at his desk.

"I will surely and definitely tame the mentally deranged US dotard with fire."

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The new penalties seek to leverage the dominance of the US financial system by forcing nations, foreign companies and individuals to choose whether to do business with the United States or the comparatively tiny economy of North Korea.

US officials acknowledged that like other sanctions, these may not deter Kim's drive to threaten the US with a nuclear weapon, but is aimed at slowing him down.

Trump's executive order grants the Treasury Department additional authority that Trump said would help cut off international trade and financing that Kim's dictatorship uses to support its banned weapons programs.

"North Korea's nuclear programme is a grave threat to peace and security in our world, and it is unacceptable that others financially support this criminal, rogue regime," Trump said in brief public remarks during a meeting with the leaders of South Korea and Japan to discuss strategy to confront Pyongyang.

He added that the US continues to seek a "complete denuclearisation of North Korea".

Significantly, Trump also said that Chinese President Xi Jinping had ordered Chinese banks to cease conducting business with North Korean entities. Trump praised Xi, calling the move "very bold" and "somewhat unexpected".

China is North Korea's chief ally and economic lifeline. Some 90 per cent of North Korean economic activity involves China, and Chinese entities are the main avenue for North Korea's very limited financial transactions in the global economy.

China is also suspected of turning a blind eye to some of the smuggling and sanctions-busting operations that have allowed Pyongyang to rapidly develop sophisticated long-range missiles despite international prohibitions on parts and technology.

All UN sanctions have to be acceptable to China, which holds veto power. China's recent willingness to punish its fellow communist state signals strong disapproval of North Korea's international provocations, but China and fellow UN Security Council member Russia have also opposed some of the toughest economic measures that could be applied, such as banking restrictions that would affect Chinese and other financial institutions.

"We continue to call on all responsible nations to enforce and implement sanctions," Trump said.

He added that the order will give Treasury Secretary Steven Mnuchin the "discretion to target any foreign bank knowingly facilitating specific transactions tied to trade with North Korea".

A White House fact sheet said that under the executive order, airplanes or ships that have visited North Korea will be banned for 180 days from visiting the United States, a move to crack down on illicit trade.

"This significantly expands Treasury's authority to target those who enable this regime . . . wherever they are located," Mnuchin said.

UN Ambassador Nikki Haley said the goal is to "cut the revenue so they could do less of their reckless behaviour".

"It doesn't mean that it will necessarily change Kim's attitude," Haley said.

Trump's announcement came as he has sought to rally international support for confronting Pyongyang during four days of meetings here at the General Assembly. In a speech to the world body on Tuesday, Trump threatened to "totally destroy" the North if necessary and referred derisively to Kim as "Rocket Man".

But the President and his aides have emphasised that they are continuing to do what they can to put economic and diplomatic pressure on North Korea to avoid a military conflict.

"We don't want war," Haley told reporters. "At the same time, we're not going to run scared. If for any reason North Korea attacks the United States or our allies, we're going to respond."

US officials say there is still time and room for diplomacy if North Korea shows that talking could be productive. Other countries, including China and Russia, are pressing Washington to make a greater effort toward talks and an eventual bargain that could buy Kim out of his weapons without toppling his regime.

The shape of a possible deal has been evident for years, but Kim has raised the stakes, and perhaps the price, with his rapid development toward the capability to launch a nuclear-equipped intercontinental ballistic missile at U.S. territory.

Asked why North Korea might entertain such an international deal when Trump appears poised to undermine a similar one with Iran, Secretary of State Rex Tillerson said a North Korea deal would be designed very differently.

"While the threat is the same - it's nuclear weapons - the issues surrounding North Korea are very different than the issues surrounding Iran," Tillerson said Wednesday. "Iran is a large nation, 60 million people; North Korea is a smaller nation, the hermit kingdom, living in isolation. Very different set of circumstances that would be the context and also the contours of an agreement with North Korea, many aspects of which don't apply between the two."

In recent weeks, the Security Council has approved two rounds of economic sanctions but also left room for further penalties. For example, the sanctions put limits on the nation's oil imports but did not impose a full embargo, as the United States has suggested it supports. The Trump administration has signaled it also wants a full ban on the practice of sending North Korean workers abroad for payments that largely go to the government in Pyongyang.

"We are witnessing a very dangerous confrontation spiral," Russian Foreign Minister Sergei Lavrov said in a speech to the United Nations, filling in for President Vladimir Putin, who skipped the forum.

"We resolutely condemn the nuclear missile adventures of Pyongyang in violation of Security Council resolutions. But military hysteria is not just an impasse; it's disaster. . . . There is no alternative to political and diplomatic ways of settling the nuclear situation on the Korean Peninsula."

Mnuchin emphasised that "this action is in no way specifically directed at China," and he said he called Chinese officials to inform them ahead of the US announcement.

Mnuchin also said the unilateral US action is not a rejection of separate Security Council sanctions and the international diplomacy they require. Similar to unilateral US sanctions on Iran applied during the Obama administration, the new US restrictions seek to leverage the power of the US financial system.

"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.

Sitting down with South Korean President Moon Jae-in before the trilateral discussion with Japan, Trump said the nations were "making a lot of progress".

Moon praised Trump's speech to the United Nations, saying through a translator that "North Korea has continued to make provocations and this is extremely deplorable and this has angered both me and our people, but the US has responded firmly and in a very good way".