North Korea has warned any provocation from the US will mean a "total war" which will lead to its "final doom".

The North accused the US of pushing the Korean peninsula to the brink of nuclear war after a pair of strategic US bombers flew training drills with the South Korean and Japanese air forces in another show of strength.

The two supersonic B-1B Lancer bombers were deployed amid rising tensions over North Korea's dogged pursuit of its nuclear and missile programmes in defiance of UN sanctions and pressure from the US.

It comes as the US military announced the Thaad missile defence system had become operational in South Korea.

North Korea said the bombers conducted "a nuclear bomb dropping drill against major objects" in its territory at a time when President Donald Trump and "other US warmongers are crying out for making a preemptive nuclear strike" on the North.

"The reckless military provocation is pushing the situation on the Korean peninsula closer to the brink of nuclear war," the North's official KCNA news agency said.

"Any military provocation against the DPRK will precisely mean a total war which will lead to the final doom of the US."

South Korean Defence Ministry spokesman Moon Sang-gyun told a briefing in Seoul that Monday's joint drill was conducted to deter provocations by the North and to test readiness against another potential nuclear test.

Trump's security adviser says North Korea will be solved 'one way or another'

The US air force said in a statement the bombers had flown from Guam to conduct training exercises with the South Korean and Japanese air forces.

Tensions on the Korean peninsula have been high for weeks, driven by concerns that the North might conduct its sixth nuclear test in defiance of pressure from the United States and Pyongyang's sole major ally, China.

Despite that, Mr Trump said he would be “honoured” to meet the North's young leader.

“If it would be appropriate for me to meet with him, I would absolutely, I would be honoured to do it,” he told Bloomberg News in comments that drew criticism in Washington.

Trump did not say what conditions would need to be met for any such meeting to occur or when it could happen, but the White House said later North Korea would need to meet many conditions before a meeting could be contemplated.

“Clearly conditions are not there right now,” White House spokesman Sean Spicer said.

“I donât see this happening anytime soon.”

Trump warned in an interview with Reuters on Thursday that a “major, major conflict” with North Korea was possible, while China said last week the situation on the Korean peninsula could escalate or slip out of control.

In a show of force, the United States has already sent an aircraft carrier strike group, led by the USS Carl Vinson, to waters off the Korean peninsula to conduct drills with South Korea and Japan.

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 Korea test-launched a missile on Saturday that appeared to have failed within minutes, its fourth successive failed launch since March. It has conducted two nuclear tests and a series of missile-related activities at an unprecedented pace since the beginning of last year.

The North is technically still at war with the South after their 1950-53 conflict ended in a truce, not a treaty, and regularly threatens to destroy the United States, Japan and South Korea.