Kim's warning follows a meeting between South Korea and the United States last week in Washington, where they discussed nuclear deterrence in the event of conflict with the North.

The meeting's agenda included "nuclear and strategic planning", and the allies reiterated that any nuclear attack by Pyongyang on the United States or South Korea would result in the end of the North Korean regime.

But Kim told his military's missile bureau "not to hesitate (launching) even a nuclear attack when the enemy provokes it with nukes," Pyongyang's official Korean Central News Agency said Thursday.

Washington, Seoul and Tokyo released a statement shortly afterwards, urging the nuclear-armed country to "stop conducting further provocations and accept our call for engaging in substantive dialogue without preconditions".

The three countries have ramped up defence cooperation in the face of a record-breaking series of weapons tests by Pyongyang this year, and on Tuesday activated a system to share real-time data on North Korean missile launches.

The North on Monday launched its most powerful intercontinental ballistic missile, the Hwasong-18, later describing it as "a warning counter-measure" against what it described as persistent acts of "military threat" by Washington and its allies.

Last week, a US nuclear-powered submarine arrived in the South Korean port city of Busan, and on Wednesday, Washington flew its long-range bombers in drills with Seoul and Tokyo.

The North has recently stressed that the "Korean peninsula is in a state of war by law" and that "strategic assets" deployed by Washington in the South will be "the first targets of destruction".

In October, when a US B-52 bomber capable of carrying nuclear weapons took part in Seoul, Tokyo and Washington's first joint aerial drills, Pyongyang described the exercise as "the intentional nuclear war provocative moves of the US".

Pyongyang sees drills by the United States and its allies as rehearsals for invasion and has long justified its blitz of missile launches as necessary "countermeasures".

- 'Preparations for invasion' -

Pyongyang last year declared itself an "irreversible" nuclear power and has repeatedly said it will never give up its nukes programme, which the regime views as essential for its survival.

In a separate statement on Thursday, Kim's powerful sister, Kim Yo Jong, slammed the United Nations Security Council for convening a session to discuss the North's latest ICBM launch, arguing it was a demonstration of Pyongyang's inherent right to self-defence.

"The ceaseless military drills of the US and its vassal forces (remind) one of the overall preparations for invasion under the pretext of deterring threats from someone," she said, according to KCNA.

"And the frequent appearance of the US nuclear weapons clearly (aimed) at the DPRK ... is the root cause of escalating the regional situation," she added, using the acronym for the North's official name.

Pyongyang's launch of a military spy satellite last month, which it claimed quickly began providing images of US and South Korean military sites, further damaged inter-Korean ties.

The launch fractured a military agreement between the Koreas established to de-escalate tensions on the peninsula, with both sides then ramping up security along the Demilitarized Zone (DMZ) that separates them.