The communist state accused Seoul “warmongers” of whipping up hysteria and confrontation over two deadly frontier incidents last year.
Relations have been icy since the South accused the North of torpedoing a warship in March 2010 with the loss of 46 lives.
Tensions rose further after the shelling of the South’s Yeonpyeong island, which killed four people including civilians.
The South demands its neighbour accept the blame for both incidents before relations can improve.
But Thursday’s statement, from the inspection group of the North’s most powerful body the National Defence Commission, repeated denials of involvement in the warship’s sinking near the disputed Yellow Sea borderline.
It also reiterated claims that the South provoked the island bombardment by staging its own artillery drill, which dropped shells into waters claimed by Pyongyang.
“The South Korean authorities and puppet military warmongers should properly understand that they are standing at the crossroads where they should choose between dialogue and war,” the statement said.
The South’s military said it was open to talks if the North suggested them, but warned of tough punishment for any fresh attacks.
Defence Minister Kim Kwan-Jin also insisted the North apologise for last year’s incidents — an issue which led to the breakdown of military talks in February.
“If North Korea launches another military attack, our military will swiftly and strongly punish the enemy’s forces until they surrender,” he said in a televised debate.
The South has strengthened border defences so it could immediately strike “the sources of attack as well as its supporting forces”, Kim said.
Earlier in the day, the South announced it would allow a private group to send aid across the border for the first time since last November.
The unification ministry, which must by law authorise cross-border contacts, said it has approved a request by the Eugene Bell Foundation to send tuberculosis medicine to the North worth 336 million won ($305,000).
The foundation, dedicated to providing medical aid to the North, is a US group with a South Korean subsidiary.
A United Nations report last week painted a dire picture of the humanitarian situation in the impoverished state.
“There have been voices that at least civic groups should be allowed to send aid to North Korea. The government has taken these factors into account,” Yonhap news agency quoted a ministry official as saying.
The ministry would consider other requests by relief groups to send humanitarian aid, the unidentified official was quoted as saying.
The World Food Programme and other UN agencies said in their report last week that more than six million Northerners urgently need food assistance.
The North has appealed to the United States and a variety of other countries for food aid.
In a change of tack this year, it has also been calling for dialogue with the South — but refuses to accept responsibility for last year’s deaths.
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