South Korea proposed Tuesday that the two sides should meet at the border truce village of Panmunjom for discussion on Kim Jeong-Wook, who was captured in the North last October.
In a reply two days later, the North insisted that Kim's fate should not be the object of debate because he broke the country's law and was punished in accordance with it, the South's unification ministry said in a statement.
Fellow activists and missionaries said Kim had been providing shelter and food to North Korean refugees living in China's northeastern border city of Dandong.
They said Kim had crossed the border to establish the whereabouts of some North Korean refugees arrested in Dandong by Chinese authorities and repatriated.
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Although religious freedom is enshrined in the North's constitution, it does not exist in practice. Religious activity is restricted to groups linked to the government.
A number of missionaries - mostly US citizens - have been arrested in the isolated communist state in the past. Some were allowed to return home after interventions by high-profile US figures.
US citizen Kenneth Bae, described by a North Korean court as a militant Christian evangelist, was sentenced last year to 15 years' hard labour on charges of trying to topple the government.
The North is known to be currently holding two other US citizens, both tourists arrested this year.