US Secretary of State Rex Tillerson has said "global action" is required to stop the "global threat" posed by North Korea as tensions rose following the rogue state's successful test of its first intercontinental ballistic missile (ICBM).

Ratcheting up the pressure on Pyongyang, Mr Tillerson said the US would "enact stronger measures" against the North, adding Washington would never accept it as a nuclear power.

South Korea also warned the North's leadership would face "destruction" as it and the US carried out tests of missiles with "deep-strike, precision capability".

North Korean leader Kim Jong-un said that its ICBM test-firing completed the country's strategic weapons capability, adding that it would not negotiate with the United States to give up the long-range missiles until Washington abandoned its hostile policy against the North, the country's KCNA news agency said. Mr Kim was said to have described the missile as a "gift" for the "American bastards".

Mr Tillerson's statements were the first official confirmation that the US authorities believe the North's claim about its ICBM capabilities to be true. He said the US would discuss its proposals at the United Nations Security Council and a meeting was due to take place on Wednesday.

"Global action is required to stop a global threat," Mr Tillerson said.

"Any country that hosts North Korean guest workers, provides any economic or military benefits, or fails to fully implement UN Security Council resolutions is aiding and abetting a dangerous regime."

The US "will never accept a nuclear-armed North Korea", he stressed.

The US Department of Defence backed up Mr Tillerson's remarks with bullish talk of its own.

"We remain prepared to defend ourselves and our allies and to use the full range of capabilities at our disposal against the growing threat from North Korea," said Pentagon spokeswoman Dana White.

"Our commitment to the defence of our allies, the Republic of Korea and Japan, in the face of these threats, remains ironclad."

In a further sign of the increased tensions, the US and South Korea conducted an offensive ballistic missile drill early on Wednesday, defying a call for a freeze on such activity by Russia and China.

The American military said the exercise – which fired missiles into the sea off South Korea's coast – demonstrated "deep strike precision capability".

In a statement about the missile drill, the office of the South Korean President, Moon Jae-in, said: "President Moon said North Korea's serious provocation required us to react with more than just a statement and that we need to clearly show our missile defense readiness to North Korea."

South Korea's military also warned the North's leadership would face "destruction" if it threatened the security of the South or its allies, the Yonhap news agency reported.

The US President and his South Korean counterpart met in Washington this week to discuss further sanctions against the North with Donald Trump saying the “era of strategic patience with the North Korean regime has failed”.

Efforts by Russia and China to ease tensions were set out in a joint statement from the two countries' foreign ministries, issued shortly after President Vladimir Putin and Chinese President Xi Jinping held talks in the Kremlin.

“The situation in the region affects the national interests of both countries,” it said.

“Russia and China will work in close coordination to advance a solution to the complex problem of the Korean Peninsula in every possible way.”

The statement said Washington was using North Korea as a pretext to expand its military infrastructure in Asia and risked upsetting the strategic balance of power in the area.

In pictures: North Korea military drill Show all 8 1 /8 In pictures: North Korea military drill In pictures: North Korea military drill North Korea's leader Kim Jong Un watches a military drill marking the 85th anniversary of the establishment of the Korean People's Army (KPA) KCNA/Handout via REUTERS In pictures: North Korea military drill A military drill marking the 85th anniversary of the establishment of the Korean People's Army (KPA) is seen in this handout photo by North Korea's Korean Central News Agency (KCNA) KCNA/Handout via REUTERS In pictures: North Korea military drill A military drill marking the 85th anniversary of the establishment of the Korean People's Army (KPA) is seen in this handout photo by North Korea's Korean Central News Agency (KCNA) KCNA/Handout via REUTERS In pictures: North Korea military drill A military drill marking the 85th anniversary of the establishment of the Korean People's Army (KPA) KCNA/Handout via REUTERS In pictures: North Korea military drill A military drill marking the 85th anniversary of the establishment of the Korean People's Army (KPA) KCNA/Handout via REUTERS In pictures: North Korea military drill This image made from video of still images broadcast in a news bulletin by North Korea's KRT, shows what was said to be a 'Combined Fire Demonstration' held to celebrate the 85th anniversary of the North Korean army, in Wonsan, North Korea. KRT via AP Video In pictures: North Korea military drill This image made from video of still images broadcast in a news bulletin by North Korea's KRT, shows what was said to be a 'Combined Fire Demonstration' held to celebrate the 85th anniversary of the North Korean army, in Wonsan, North Korea. KRT via AP Video In pictures: North Korea military drill This image made from video of still images broadcast in a news bulletin by North Korea's KRT, shows what was said to be a 'Combined Fire Demonstration' held to celebrate the 85th anniversary of the North Korean army, in Wonsan, North Korea. KRT via AP Video

North Korean state television said the test of the Hwasong-14, which took place early on Tuesday morning local time, was overseen by the country's leader. It said the projectile had reached an altitude of 1,731 miles and flew for 39 minutes before hitting a target in the sea.

It added North Korea was now a “full-fledged nuclear power that has been possessed of the most powerful intercontinental ballistic rocket capable of hitting any part of the world”.

The North's state-run KCNA news agency reported that after Mr Kim witnessed the tests "he said American bastards would be not very happy with this gift sent on the July 4 anniversary".

Experts said the capabilities of the missile remained unclear — with some disgreement over the potential range of the missile — but said it marked a potential milestone in North Korea’s efforts to project its nuclear capability.

David Wright, of the Global Security Programme at the Union of Concerned Scientists, said if the reports were true, the missile would have a maximum range of around roughly 4,160 miles on a standard trajectory.

“That range would not be enough to reach the lower 48 states or the large islands of Hawaii, but would allow it to reach all of Alaska,” he said in a blog post.

Karl Dewey, an analyst with Jane’s Information Group, said a successful development of an ICBM by North Korea, would “give decision-makers in Washington reason to pause for thought before deciding to strike the communist regime”.

Some have suggested the missile could even travel further, if launched in an easterly direction given the Earth’s rotation. This would technically enable North Korea to target not just all of Alaska, but a small part of northwestern Canada.

Jean Lee of Wilson Centre in Washington said the latest test was cause for people to be worried. “Test-firing a ballistic missile just days after the Trump-Moon summit, where the two leaders discussed tightening sanctions against North Korea, is Pyongyang’s way of sending a message of defiance to the US and South Korean leaders,” she said.

“It’s also strategic: if the US and South Korea are going to step up sanctions, North Korea will certainly move faster in getting its illicit nuclear and ballistic missile programmes as far along as they can before any negotiations on a freeze or dismantlement.”