President Donald Trump has dismissed China’s efforts to try and rein in the North Korean regime of Kim Jong-un, saying that a recent visit seemed to have “no impact” on the nuclear ambitions of Pyongyang.

The barbs come on the heels of North Korea’s latest missile launch, and a day after speaking with China’s President Xi Jinping and reiterating the need for China to use its leverage of North Korea’s largest trading partner to increase pressure on the regime.

“The Chinese envoy, who just returned from North Korea, seems to have had no impact on Little Rocket Man,” Mr Trump tweeted, referring to this nickname for Mr Kim. The insulting rhetoric, with Mr Trump having also called the North Korean leader “a sick puppy”, perhaps reflects the President’s frustration that Pyongyang was able to test-fire its most advanced ballistic missile earlier this week.

State media proclaimed the launch of the intercontinental ballistic missile (ICBM) as a “breakthrough” that put it on track to be able to hit the US mainland – as it also looks to perfect its nuclear warhead technology. White House Press Secretary Sarah Huckabee Sanders said in a briefing later in the day that the US is focused on “one big thing” in relation to North Korea and that is denuclearisation.

A number of rounds of sanctions from the UN has done little to stop Pyongyang pushing on with its nuclear and missile programmes, with the latest launch also pushing US Ambassador to the UN, Nikki Haley, to suggest that the regime of Mr Kim would be “utterly destroyed” if Washington was pushed into war.

Ms Haley told a meeting of the UN Security Council: “We have never sought war with North Korea, and still today we do not seek it ... If war comes, make no mistake, the North Korean regime will be utterly destroyed.”

While Mr Trump has repeatedly suggested he could resort to military action if North Korea does not bend to international will, administration officials have said that diplomatic recourse is the preferred option. Mr Trump has repeatedly called on China to do more about North Korea and Beijing had dispatched the envoy mentioned in the tweet earlier this month – after Mr Trump travelled to China as part of a recent tour of Asia.

A sign of that push for diplomacy was given by US Secretary of State Rex Tillerson, who welcomed Chinese efforts on North Korea on Thursday, but said Beijing could do more to limit its oil exports to the country.

“The Chinese are doing a lot. We do think they could do more with the oil. We’re really asking them to please restrain more of the oil, not cut it off completely,” Mr Tillerson said at the State Department.

The launch was the first test the hermit kingdom has conducted in two months, the last coming on 15 September when an ICBM was sent over northern Japan.

North Korea announces test of new long-range missile

South Korea’s military says the latest missile was fired from an area north of Pyongyang early on Wednesday morning local time.

The Pentagon tracked the trajectory of the weapon and spokesman Colonel Rob Manning said the missile was launched from Sain Ni, North Korea, and travelled about 620 miles (1,000 km) before landing in the Sea of Japan.

It also reportedly went approximately 2,800 miles (4,000 km) up into the atmosphere, according to South Korean and Japanese authorities. US Defence Secretary James Mattis said the latest missile did fly higher than previous ones.

He warned that North Korea continues to strengthen its nuclear weapons programme with weapons that “threaten everywhere in the world”.

Mr Mattis added on Thursday that US diplomats are in a strong position as “we do have military options” and that those diplomats would be “unrelenting” in their work through the UN.

North Korea announces intercontinental missile launch Show all 13 1 /13 North Korea announces intercontinental missile launch North Korea announces intercontinental missile launch Pyongyang residents react after the news of the successful launch of the new intercontinental ballistic missile AFP/Getty Images North Korea announces intercontinental missile launch North Korea's leader Kim Jong Un signing an order to test-fire the newly developed inter-continental ballistic missile KRT via AP Video North Korea announces intercontinental missile launch A news broadcast displays Kim Jong Un's signed document AP North Korea announces intercontinental missile launch People cheer as they watch the news broadcast announcing Kim Jong Un's order to test-fire the new inter-continental ballistic missile AFP/Getty Images North Korea announces intercontinental missile launch Residents react after the document signing AP North Korea announces intercontinental missile launch Pyongyang residents celebrate Kim Jong Un's announcement AFP/Getty North Korea announces intercontinental missile launch Cheering Pyongyang residents react AP North Korea announces intercontinental missile launch To counter North Korea's missile test, South Korea fired missiles into the East Sea The Defence Ministry/Yonhap via REUTERS North Korea announces intercontinental missile launch The Hyunmu-2 missiles firing during the drill South Korean Defense Ministry vi North Korea announces intercontinental missile launch The exercise was carried out in an attempt to counter Kim Jong Un's order South Korea Defense Ministry via AP North Korea announces intercontinental missile launch The South Korean army continue to carry out military exercises AP North Korea announces intercontinental missile launch Where K-9 self-propelled howitzers were taking part in a drill Rex Features North Korea announces intercontinental missile launch US soldiers are also present in the border city of Paju AFP/Getty Images

The US had recently put North Korea back on the list of nations that sponsor terrorism. Mr Tillerson said at the time that the move was “very symbolic ... Practical effects may be limited but hopefully clos[es] off loopholes” in existing sanctions for “dual use” product exports that can be used by civilians and the military.

North Korea was last on the state-sponsored terror list in 2008, under the George W Bush administration. It was removed that year in a bid to salvage a deal halting its nuclear development programme.

On Thursday, ​Russian Foreign Minister Sergei Lavrov called Washington’s approach dangerously provocative and said that joint US-South Korean military exercises planned for December could provoke Mr Kim into “flying off the handle”.

He also flatly rejected a US call for all nations to “cut ties” with Pyongyang, which Ms Haley had made at the UN, calling US policy toward North Korea deeply flawed.

In a call with Mr Trump in the afternoon, South Korean President Moon Jae-in said the missile launched this week was North Korea’s most advanced so far, but it was unclear whether Pyongyang had the technology to miniaturise a nuclear warhead and it still needed to prove other things, such as its re-entry technology.

A White House statement said Mr Trump and Mr Moon reiterated their strong commitment to enhancing the deterrence and defense capabilities of both nations.

Meanwhile, German Foreign Minister Sigmar Gabriel said after meeting Mr Tillerson that he had offered support for taking a tough line towards North Korea and that Germany was withdrawing a third diplomat from its embassy there.