Kim also promised that the North would follow a policy of non-proliferation, and said Pyongyang was willing to improve and normalise relations with countries that had been "hostile" in the past.
His remarks came in a report delivered on the second day yesterday of the first Workers' Party congress to be held since 1980.
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It was the North's fourth nuclear test, and there are growing signs that a fifth test could be imminent.
"As a responsible nuclear weapons state, our republic will not use a nuclear weapon unless its sovereignty is encroached upon by any aggressive hostile forces with nukes," Kim was quoted as telling the party gathering yesterday.
He also vowed that Pyongyang would "faithfully fulfil" its non-proliferation obligations and push for global denuclearisation, the North's official KCNA news agency said.
North Korea withdrew from the global Non-proliferation Treaty (NPT) in 2003 -- the first signatory country to do so.
Pyongyang's nuclear weapons use policy has never been completely clear.
At the time of the first nuclear test in 2006, North Korea stated it would "never use nuclear weapons first", but has since made repeated threats of pre-emptive nuclear strikes against South Korea and the United States.
Kim's latest statement does not seem to amount to a clear "no first-use" policy, as it does not specify what kind of "encroachment" might justify a nuclear strike.
In recent years, North Korea has put a focus on the development of tactical nuclear weapons, with numerous -- and increasingly successful -- tests of a submarine-launched ballistic missile system.
In his address, Kim also waved what might be taken as a potential olive branch, with his statement that North Korea would seek better relations with friendly countries, "(even) though they had been hostile in the past."
There has been speculation that, in the wake of the party congress, Pyongyang might renew its push for talks with Washington.
US and North Korean officials have held a number of informal discussions in neutral venues in recent years, but they are understood to have stalled over the basis for beginning any substantive dialogue.
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