Inter-Korean talks in Pyongyang have been suspended after the North's warning that Seoul faced "unspeakable disaster" if it sided with Washington in the nuclear crisis.
North Korea frequently issues aggressive rhetoric
The South Korean delegation said it wanted an explanation and apology before talks continued on Wednesday.
The North Koreans have been angered by an apparent hardening of South Korean policy towards Pyongyang after a recent visit to the US by South Korean President Roh Moo-hyun.
Seoul and Washington threatened, during their talks, to take "further steps" against Pyongyang, if it continued to escalate tensions on the peninsula with its suspected development of nuclear weapons.
The inter-Korean talks, which started on Tuesday, were due to discuss progress on joint economic problems, including reconnecting cross-border roads and railways, constructing an economic zone in the North and providing rice and fertiliser aid to the Pyongyang.
South Korea is said to have also wanted to discuss the nuclear crisis, before the controversial comments on Tuesday by the chief North Korean delegate Pak Chang-ryon.
Pride at stake
Mr Chang-ryon had warned: "The South side will sustain an unspeakable disaster if it turns to confrontation.
"Should the South take the path of confrontation, talking about the so-called nuclear issue or 'further steps'... North-South ties would come to naught."
The head of the South Korean delegation, Kim Gwang-lim, said the South should not respond emotionally, but added that it should not throw away its pride by clinging to the talks at all costs.
We do want an apology, or some sort of explanation, though an apology may be too much to expect
South Korea Unification Ministry
He warned that the North risked losing the gains from joint economic exchanges by escalating tensions in the crisis.
The BBC's Caroline Gluck said Southern officials were taken aback, not just by the strength of the North's attack, but by the fact that it was issued directly by the head Northern delegate to the talks, rather than indirectly through the North's state-controlled media.
Kim Jung-Ro, deputy spokesman at South Korea's Unification Ministry, which handles North Korean affairs said: "We are not going to walk out unless North Korea makes further threats.
"But we do want an apology, or some sort of explanation, though an apology may be too much to expect."
South Korea's main opposition party has demanded that Seoul recall its economic
The Grand National Party said in a statement: "North Korea is threatening us while demanding rice aid, so the South must stop the talks and pull out."
North Korea's relations with the South and the US have been at boiling point since last October, when Washington said Pyongyang had admitted to a secret nuclear weapons programme.
The North appears to have been angered by the threat of "further steps" in the joint statement issued by the US and South Korea after the Washington summit.
It was not clear what those "further steps" were, but they could include the adoption of sanctions, or even military action.
Meanwhile, two men who are said to be North Korean defectors have appeared before a sub-committee of the US Senate to disclose their alleged involvement with Pyongyang's nuclear programme.
The men, who used aliases, were led in wearing black hoods, and gave evidence behind a tall screen.
One of them said 90% of the parts used in the nuclear programme were smuggled through informal channels from Japan.
The other man alleged North Korea used illicit heroin exports to gain foreign exchange.