Kim made the comments Monday at a university, in a speech which was printed in full by state media KCNA on Tuesday.
He mentioned South Korean President Yoon Suk-yeol by name for the second time in a week in denouncing Seoul for colluding with Washington to destabilise the region to gloss over the fact it does not even have proper strategic weapons.
"Yoon Suk-yeol made some tasteless and vulgar comment about the end of the Republic in his speech, and it shows he is totally consumed by his blind faith in his master's strength," KCNA quoted Kim as saying, referring to the South's alliance with the United States.
"To be honest, we have absolutely no intention of attacking South Korea," he said in the speech at the Kim Jong-un National Defence University, a training ground for elite military specialists.
"Every time I stated our position on the use of military force, I clearly and consistently used the qualification 'if.'
"If the enemies try to use force against our country, the Republic's military will use all offensive power without hesitation. This does not preclude the use of nuclear weapons.
"Our footsteps towards becoming a military superpower and a nuclear power will accelerate."
North Korea has for decades pursued a nuclear weapons program and is believed to have enough fissile materials to build dozens of the weapons. It has conducted six underground nuclear detonation tests.
Last week, South Korea marked an annual armed forces day with a large military parade showcasing a ballistic missile capable of carrying a massive warhead and featuring a fly-past of a US strategic bomber.
In his address that day, Yoon warned the North against using nuclear weapons.
"That day will see the end of the North Korean regime," he said.
KCNA said Kim made the remarks on Monday, the same day the North has said its Supreme People's Assembly would meet to discuss amending the country's constitution. The news agency has made no mention of the assembly's deliberations since Monday.
The session is being closely watched because of the likelihood it would approve a constitutional amendment to reflect Kim's statement that unification is no longer possible and the South was a separate country and "a principal enemy."
Such a move would formalise Kim's break with decades-old goal espoused by both countries of national unification and attempts to improve ties, including a 2018 summit where their leaders declared there will be no more war and a new era of peace has opened.
In a separate report, KCNA said Kim sent a birthday message to Russian President Vladimir Putin, calling him his "closest Comrade and saying "strategic and cooperative relations" between the two countries will be raised to a new level.
