Kim Jong-Un's North Korea says it will speed up its nuclear programme Photo: Courtesy

Donald Trump says he would be 'honoured' to meet North Korea's leader Kim Jong Un.

"If it would be appropriate for me to meet with him, I would absolutely, I would be honoured to do it,'' the president told Bloomberg in an interview, adding, "under the right circumstances I would meet with him."

Following the interview, the White House said 'the conditions are not there at this time' for such a meeting to take place.

A spokesman added that the US would 'need to see North Korea's provocative behaviour ratcheted down immediately'.

The president's statement comes as North Korea warned it will fire more nuclear missile tests “at any time,” amid escalating tension with America.

The rogue state said it will bolster its nuclear force "to the maximum" as the America builds up its military in the Korean Peninsula.

Pyongyang's foreign ministry said the country: “...will speed up at the maximum pace the measure for bolstering its nuclear deterrence.”

Trump threatened over the weekend a "major, major conflict" and his National Security Advisor warned of “military action.”

Lieutenant General HR McMaster said North Korea's war threats: “...may mean ratcheting up those sanctions even further and it also means being prepared for military operations if necessary."

North Korea's foreign ministry threats were made as America's powerful USS Carl Vinson carrier fleet deployed to the region.

American commanders have begun installing their controversial Terminal High Altitude Area missile defence system in South Korea to prepare for war.

Reclusive North Korea has carried out five nuclear tests and a series of missile tests in defiance of U.N . Security Council resolutions.

It has been conducting tests at an unprecedented rate and is believed to be close to developing intermediate-range and submarine-launched missiles.

North Korea launched another missile test over the weekend which was branded unsuccessful by Seoul and Washington but was heavily criticised by the west.

American is appealing to China to mediate with North Korea over the threat of war and tension over Kim Jong-Un's repeated missile tests.

Tension has been high in the region over fears North Korea will try and fire a long-range missile test or a sixth nuclear test- since the April 15 anniversary of the state's founder's birth.

North and South Korea have been at war since their 1950-53 conflict ended with truce but not a treaty, meaning technically they are still at war.

North Korea has repeatedly threatened nuclear war against America.