Pyongyang urged Seoul on Monday to bring four North Korean would-be defectors to the border so they can confirm in front of their families that they want to stay in South Korea.
The South refuses to return four of 31 North Koreans whose fishing boat drifted across the border in thick fog last month, saying the two men and two women have freely chosen to stay.
The case is the latest in a series of disputes which have kept tensions high for the past year. It comes amid US and South Korean military exercises that the North has branded a rehearsal for invasion.
The North says the South used "appeasement and deception" to try to force members of the group to defect in an attempt to fuel cross-border tensions.
The South tried to hand over the other 27 at the frontier village of Panmunjom on Friday, but the North refused to accept them and insisted that all 31 be returned.
On Monday its state-controlled Red Cross proposed a meeting at Panmunjom on Wednesday to arrange "the early repatriation of all of those in custody", the North's official news agency reported.
It said three Pyongyang officials would be accompanied by the families of the four, and asked Seoul to bring the apparent defectors along to the meeting.
Lee Hae-Young, secretary general of the Seoul-based association of North Korean Defectors, said families of defectors customarily face reprisals — possibly a spell in a prison camp or forced relocation to a rural area.
The families of the four might be induced to attend a border meeting through pressure or promises to soften reprisals somewhat, he told AFP.
The North described the defection claim as false and said the South's "outrageous inhuman action" was sparking anger and concern about the impact on cross-border relations.
It said the four people in question had no reason whatever to defect "in light of their socio-political circumstances and family background".
The South, in its reply, said it was willing to hold talks but the four would not be present.
"We won't produce them at the meeting because the free will of the four has been confirmed by objective and fair measures," said unification ministry spokeswoman Lee Jong-Joo.
The South also said it intends to return the 27 others on Monday afternoon and asked the North to receive them. But the ministry said there had been no response as of early evening.
A special investigation team from the US-led United Nations command, which supervises the armistice in place since the 1950-53 Korean War, has interviewed the four about their intentions.
"It came to the conclusion that they have decided to remain in (South Korea) of their own free will," said US forces spokesman David Oten.
North Korea on Monday protested at the US forces' "despicable" act in backing South Korea in the case. Their stand represents "inhumane criminal behaviour", it said.
The four are the 38-year-old boat captain, a 21-year-old female nurse, a 44-year-old unemployed man and a 22-year-old female statistician.
Relations have been icy since the South accused the North of torpedoing a warship in March 2010 near the disputed Yellow Sea border with the loss of 46 lives. Pyongyang denies the charge.
In November the North shelled a South Korean island near the border, killing two marines and two civilians.
More than 20,000 North Koreans fleeing their impoverished homeland have arrived in the South since the end of the 1950-1953 war, mostly via China.