China has repeatedly called for restraint on the peninsula.
The North has been threatening to attack the South and U.S. military bases almost on a daily basis since the beginning of March, when U.S. and South Korean militaries started routine drills that have been conducted for decades without incident.
Many in the South have regarded the North’s willingness to keep open the Kaesong industrial zone, located just a few miles (km) north of the heavily-militarised border, as a sign that Pyongyang will not risk losing a lucrative source of foreign currency by mounting a real act of aggression.
The Kaesong zone is a vital source of hard currency for the North and hundreds of South Korean workers and vehicles enter daily after crossing the armed border.
“If the puppet traitor group continues to mention the Kaesong industrial zone is being kept operating and damages our dignity, it will be mercilessly shut off and shut down,” KCNA quoted an agency that operates Kaesong as saying in a statement.
Closure could also trap hundreds of South Korean workers and managers of the more than 100 firms that have factories there.
The North has previously suspended operations at the factory zone at the height of political tensions with the South, only to let it resume operations later.
North Korea has cancelled an armistice agreement with the United States that ended the Korean War and cut all hotlines with U.S. forces, the United Nations and South Korea.
(Additional reporting by Sung-won Shim and Jane Chung; Editing Rosalind Russell and Jon Boyle)