The US ambassador to the United Nations says the UN Security Council has run out of options to contain North Korea's nuclear program, adding Washington may have to turn the matter over to the Pentagon.

Key points: Ms Haley says if North Korea continues it "will be destroyed"

Ms Haley says if North Korea continues it "will be destroyed" Donald Trump calls Kim Jong-un "rocket man" and praises sanctions effects

Donald Trump calls Kim Jong-un "rocket man" and praises sanctions effects Security adviser HR McMaster says preparing a military option is becoming necessary

"We have pretty much exhausted all the things that we can do at the Security Council at this point," Nikki Haley told CNN, adding that she was perfectly happy to hand the North Korea issue over to Defence Secretary James Mattis.

As world leaders head to the United Nations headquarters in New York for the annual General Assembly meeting this week, Ms Haley's comments indicated the US was not backing down from its threat of military action against North Korea.

On Thursday, North Korea launched a missile over Japan into the Pacific Ocean in defiance of new UN Security Council sanctions banning its textile exports and capping imports of crude oil.

China has urged the US to refrain from making threats to North Korea, but when asked about President Donald Trump's warning last month that the North Korean threat to the US will be met with "fire and fury", Ms Haley said "it was not an empty threat".

"If North Korea keeps on with this reckless behaviour, if the United States has to defend itself or defend its allies in any way, North Korea will be destroyed," she said.

"And we all know that. And none of us want that. None of us want war.

"We're trying every other possibility that we have, but there's a whole lot of military options on the table."

Pyongyang has launched dozens of missiles as it accelerates a weapons program designed to provide the ability to target the US with a powerful, nuclear-tipped missile.

On Saturday, North Korea warned that it was nearing its goal of reaching "equilibrium" in military force with the US.

Mr Trump is reportedly planning to meet with South Korean President Moon Jae-in on the sidelines of the UN General Assembly.

On Sunday, Mr Trump took to Twitter to ask how "rocket man" was doing, presumably referring to Kim Jong-un's increasing missile launches.

"I spoke with President Moon of South Korea last night. Asked him how Rocket Man is doing. Long gas lines forming in North Korea. Too bad!"

'We're out of road', McMaster warns

Sorry, this video has expired North Korea has launched a series of missiles in recent months

On Friday, White House national security adviser HR McMaster said that after the latest North Korean missile launch, the United States was running out of patience: "We've been kicking the can down the road, and we're out of road."

But on Sunday, Mr McMaster warned of imminent danger from Pyongyang.

"This regime is so close now to threatening the United States and others with a nuclear weapon, that we really have to move with a great sense of urgency on sanctions, on diplomacy and preparing, if necessary, a military option," Mr McMaster told Fox News.

Military options available to Mr Trump range from a sea blockade aimed at enforcing sanctions to cruise missile strikes on nuclear and missile facilities to a broader campaign aimed at overthrowing leader Kim Jong-un.

Mr Mattis has warned the consequences of any military action would be "tragic on an unbelievable scale" and bring severe risk to US ally South Korea.

Democratic US senator Dianne Feinstein said on Sunday that Mr Trump should not rule out talks with North Korea before it agrees to end its nuclear program.

"I think that North Korea is not going to give up its program with nothing on the table," she said on CNN.

Ms Feinstein said that a freeze of both its nuclear program and missile arsenal, rather than ending them, would be more palatable to North Korea and to China, who fears the US goal is toppling Kim.

The US still wants a peaceful solution and has been waiting for the North Koreans to indicate they are ready to talk, Secretary of State Rex Tillerson said on CBS' Face the Nation.

"We have tried a couple of times to signal to them that we're ready, when they're ready," he said.

"And they have responded with more missile launches and a nuclear test."

Nikki Haley (L) and security chief HR McMaster both expressed considerations for military options on Sunday. ( AP: Carolyn Kaster, file )

Reuters