HONG KONG (BLOOMBERG) - US President Donald Trump has regularly called on China to stop North Korea's nuclear advancement, even saying in July it could "easily" end the crisis.

In Beijing, however, leaders think the opposite.

While the United States and China agree the Korean peninsula should be rid of nuclear weapons, they differ on how best to achieve that.

The sense of urgency is heightened in Washington, as the US suddenly finds itself potentially in range of North Korean leader Kim Jong Un's nuclear weapons, whereas China and the North's other neighbours have lived with the threat for years.

Mr Trump has said China should use its economic leverage as North Korea's top trading partner to quickly end Kim's nuclear ambitions.

China, however, sees no need to trigger a potential catastrophe on its border over what it regards as fundamentally a dispute between the US and North Korea. Indeed, Beijing has warned that rhetoric from both sides - the US has threatened military action against North Korea - is making things worse.

In China's eyes, Mr Kim would not give up his nuclear arsenal even if Beijing shuts off its oil supply - despite the economic pain that could cause. That is because his weapons programme gives him a deterrent against the US, which North Korea frequently says wants to attack it.

It also is central to his ability to hold onto power at home by presenting an image of ultimate strength and control to North Koreans, including his generals.

The only way Mr Kim may stop, the thinking goes, is for the US to offer him a security guarantee, such as signing a legally binding non-aggression treaty.

But former US negotiator Christopher Hill says the US is concerned that, even with a treaty, the regime cannot be trusted not to use its weapons to attack a US ally such as South Korea.

"Without holding the key to the DPRK's security concerns, China has no leverage to convince this foreign nation to stop its nuclear programme," Ms Fu Ying, chairman of the Foreign Affairs Committee of China's legislature, wrote in a May paper for the Brookings Institution, using the initials for North Korea's formal name.

"The US, which the DPRK sees as the source of threats to its security, has been neither interested nor willing to consider responding to the DPRK's security concerns," Ms Fu said.

China's logic extends to the current debate at the United Nations Security Council, where the US has proposed to cut off North Korea's oil supply after it conducted its sixth and most powerful nuclear test.

China has repeatedly said it will support further UN action if it helps restart talks with North Korea. Unlike Mr Trump, Beijing's leaders fundamentally oppose a war to resolve the situation.

"China has reiterated many times that military force cannot be an option for the settlement of the Korean Peninsula nuclear issue," Foreign Ministry spokesman Geng Shuang said the day after North Korea detonated what it called a hydrogen bomb. A "peaceful solution will be the only correct way."

North Korea's state-run Korean Central News Agency accused the US of having carried out tests of nuclear bombs and missiles while decrying similar actions by Pyongyang.

"It is the gangster-like logic that cannot convince anyone," KCNA said in a Saturday commentary. "Its talking about war and threat of harsh sanctions will enhance only the Korean people's revolutionary consciousness and add justification to the DPRK's access to nukes."

China has backed North Korea since the Korean War, in part to have a buffer state that keeps US military forces from sitting on its border.

While Mao Zedong once described ties as being as "close as lips and teeth", the relationship has become strained since Mr Kim and Chinese President Xi Jinping came to power, and some China observers say Mr Trump is overstating Mr Xi's ability to influence what the regime does.

Mr Kim's antics have also started to affect China's strategic interests. A proliferation of missile defence systems by the US and its allies could thwart China's own military capabilities. There are environmental risks if radiation spills across its northeastern border. And Mr Kim might do something that triggers an actual war.

"China does not have the power to dictate to the DPRK," said Mr Victor Gao, who was a translator for late leader Deng Xiaoping. "And now that the DPRK is in possession of nuclear weapons, the likelihood that the Chinese could dictate any terms is even more remote."

China has sought to play a mediating role, backing progressively tougher sanctions like a ban on coal exports while proposing that both sides freeze hostilities and return to talks. Those actions, regularly dismissed as insufficient by Mr Trump's administration, have led to public spats with Pyongyang.

North Korea's state media said in February that China was "dancing to the tune of the US".

China's Communist Party-affiliated Global Times said in an August editorial that China should stay neutral if North Korea starts a war with a missile attack, but intervene if the US and South Korea seek to topple Mr Kim's regime.

"China opposes both nuclear proliferation and war in the Korean Peninsula," the paper said. "It will not encourage any side to stir up military conflict, and will firmly resist any side which wants to change the status quo of the areas where China's interests are concerned."

Since coming to power in late 2011, Mr Kim has detonated four nuclear devices, test fired some 90 missiles including two intercontinental ballistic missiles, executed his uncle and murdered his brother, both of whom were seen as close to Beijing.

Some China-based academics say Beijing's policy has enabled North Korea's nuclear buildup. International relations professor Zhu Feng at Nanjing University, wrote in Foreign Affairs in July that China should abandon support for North Korea because its nuclear program threatens regional stability.

Beijing could cut off oil supplies or halt all trade with North Korea to show its readiness to abandon Mr Kim if needed, Prof Zhu said separately in an e-mail on Sept 8. "Then it might leave Pyongyang to reconsider if their WMD risk could last," he said, a reference to weapons of mass destruction. "It seems that Pyongyang is betting on impossibility of China's full abandonment of it."

The publication of dissenting views has given rise to a school of thought that a policy change on North Korea is under discussion. Still, a day after Prof Zhu's article was published, Mr Geng from the Foreign Ministry blasted "certain people" who have played up "the so-called China-responsibility theory".

One common view in Beijing is that Mr Trump's war rhetoric has only made Mr Kim more insecure, prompting him to accelerate his weapons programme.

"Achieving the denuclearisation goal on the Korean peninsula is a complicated tango dance," said Mr Gao, who is director of the China National Association of International Studies in Beijing. "Everyone needs to tango in sync, first and foremost the US and China."