Speaking to thousands of delegates gathered for the first Workers' Party congress in more than 35 years, Kim also announced a new five-year plan to boost the impoverished country's moribund economy and "revitalise" people's lifestyles.
Preparations in 'final stages' for North Korea nuclear test: report
His remarks, published by state media on Sunday, came amid growing concerns that the North might be on the verge of conducting a fifth nuclear test.
Kim had opened the congress with a defiant defence of the North's nuclear weapons programme, praising the "magnificent... and thrilling" test of what Pyongyang claimed was a powerful hydrogen bomb on January 6.
But his report to the conclave on Saturday stressed that North Korea was also a "responsible nuclear weapons state" with an arsenal built for deterrence.
"Our republic will not use a nuclear weapon unless its sovereignty is encroached upon by any aggressive hostile forces with nukes," he said, according to an English translation of his speech by the North's official KCNA news agency.
That formula would appear to allow for the use of nuclear weapons against a conventional attack by a nuclear power, but the Korean-language version made it clear that the scenario involved an actual nuclear attack.
Kim also vowed that Pyongyang would "faithfully fulfil" its non-proliferation obligations and push for global denuclearisation.
North Korea withdrew from the global Non-proliferation Treaty (NPT) in 2003 -- the first signatory country to ever do so.
Pyongyang's nuclear weapons doctrine has always been a complex mix of self-defence, deterrence and threat.
At the time of its first nuclear test in 2006, North Korea stressed that it would "never use nuclear weapons first."
US says it will respond strongly in event of another North Korea nuclear test
And when it codified its nuclear programme in North Korea law in April 2013, it stated that nuclear weapons could only be used to repel invasion or attack by another nuclear power.
But in recent years, and especially in the wake of tough UN sanctions imposed over its fourth test in January, it has issued repeated warnings of pre-emptive nuclear strikes against South Korea and the United States.
"The survival of the ruling Kim family is intimately linked to nuclear arms because they help legitimise Kim Jong-Un's hereditary rule and keep his foreign foes at bay," said Alexandre Mansourov, an expert on North Korean security issues.
The party congress is widely seen as Kim's formal "coronation" as supreme leader, more than four years after he took power following the death of his father, late ruler Kim Jong-Il, in late 2011.
On the economic front, Kim unveiled a five-year economic plan to improve efficiency and output across key sectors, with a particular emphasis on energy.
But his report offered little in the way of specific policy initiatives or numerical targets.
"The goal ... is to revitalise people's overall livelihoods and .... lay the foundation for a sustainable improvement of the nation's economy," Kim said.
North Korea's fifth nuclear test seen imminent, increased movements at site
Kim's rule has been associated with his "byungjin" policy of pursuing nuclear weapons in tandem with economic development.
Some analysts had suggested Kim might use the congress to signal a tilt towards the economic side of the equation.
In his address, Kim also said North Korea would seek to improve and normalise relations with previously "hostile" countries.
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 Washington and Seoul insist Pyongyang must make tangible steps towards denuclearisation before any substantive dialogue can begin.
Kim has made it clear that the future of the North's nuclear weapons programme is non-negotiable.
Concern that the North might be readying a fifth nuclear test was fuelled Saturday by recent satellite imagery of activity at the Punggye-ri nuclear test site in the northeast of the country.
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