Three North Koreans wanted to defect after they were rescued from a small fishing boat which had drifted into South Korean waters off the east coast, officials said Tuesday.
A South Korean coastguard vessel rescued four fishermen and a farmer from North Korea last Saturday after their boat was found drifting across the sea border, the South's unification ministry said.
Three of them expressed a desire to stay in the South when they were picked up near the eastern island of Ulleung, while the others wanted to return home, it said in a statement.
Seoul has sent a message to Pyongyang, suggesting it would send home the two who called for repatriation through the border truce village of Panmunjom, ministry officials said.
But the North has rejected the South's offer, insisting all five should be sent home, they said.
North Korea and South Korea have a disputed maritime boundary, and encroachment by North Korean fishing vessels into waters claimed by the South is quite common.
South Korea's policy is to allow North Korean fishermen crossing into what it considers its waters to decide whether or not to return to the North.
Seoul repatriated two North Korean fishermen rescued off the east coast in February and five others last month after investigators confirmed their wish to return home.
The North usually sends home South Korean fishermen rescued in its waters, although some have been held there against their will.
On June 15, a 19-year-old North Korean soldier defected to the South through the demilitarised zone (DMZ) separating the two Koreas, which remain technically at war.
The DMZ, despite its name, is one of the world's most heavily militarised frontiers, bristling with watchtowers and landmines.
Most North Koreans who flee repression and poverty at home cross the porous frontier with China first before travelling through a Southeast Asian nation and eventually arriving in South Korea.
So far about 28,000 North Koreans have resettled in the South since the end of the 1950-53 Korean War.