Pyongyang has launched a series of missiles this year, including a Hwasong-12 intermediate-range projectile this month which the North claimed was capable of carrying a "heavy" nuclear warhead, fuelling tensions with Washington.
It has carried out two atomic tests since the beginning of last year, insisting it needs nuclear weapons to defend itself against the threat of invasion.
The US is worried that if North Korean leader Kim Jong-Un is not stopped, other countries in the region including Japan and South Korea would be compelled to seek their own nuclear capability as a defence measure.
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Australian Foreign Minister Julie Bishop told The Australian newspaper this was conveyed to her in New York, where she held meetings with the US ambassador to the UN Nikki Haley. "In my discussions with senior officials in both South Korea and the US, the view was that should North Korea ever be recognised as a nuclear weapons state, then Japan and (South) Korea would have little option than to develop their own nuclear weapons capability," she said.
"That is why there is such a strong view that North Korea must be denied this capability."
On the campaign trail last year, Trump raised the possibility of Japan and South Korea arming themselves with nuclear weapons, particularly sensitive in Japan - the only country to ever be attacked by atomic bombs - but later drew back from the remarks.
The United States says it is willing to enter into talks with North Korea if it halts its nuclear and missile tests, but it has also warned that military intervention was an option, sending fears of conflict spiraling.
Bishop said the "loud and clear" message from Haley was that "when the United States said all options are on the table, they mean it, they are not kidding", pointing to the US sending a nuclear submarine to the region.
More encouragingly, the North's main trade partner and ally China appeared to be getting onside with the global community, she added in a separate interview with radio station 2GB. "North Korea currently is rebuffing overtures from China, which is frustrating China," she said.
"In the past, it was seen as very much in the sphere of influence and a branch of their communist party. But now North Korea is being far more belligerent... offensive and making snubs to China."
The United States has for weeks been negotiating a new Security Council sanctions resolution with China. But Haley said last week that no final draft had been clinched. Bishop urged Beijing to adhere to a new sanctions regime, saying it would "change the economic scenario in North Korea and essentially bring it to the negotiating table".
"We have a window of opportunity in relation to economic sanctions and this is where we need China's support," she said.
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