The two sides also reopened an inter-Korean hotline at the truce village, signaling a thaw in relations.
An inter-Korean air-traffic hotline still exists between the two sides, according to reports.
In some of the most devastating rhetoric to emanate from the North in decades, North Korea said it would nullify the armistice signed at the end of the Korean War in 1953 and terminate its hotline with Seoul.
There was a hotline linking Seoul and Pyongyang, but North Korean leader Kim Jong Un severed the channel in 2013 and refused to restore it, said Gary Samore, a former senior White House adviser now with Harvard University's Belfer Center for Science and International Affairs.
It has also unilaterally disavowed the 1953 armistice that halted the Korean war, and refused to answer a military hotline set up between the North and South.
In recent weeks, the North has shut down an emergency military hotline between Seoul and Pyongyang and stopped South Koreans from working at a joint industrial complex in the North.
In announcing the end of the "hotline" in the truce village of Panmunjom, where the Korean War armistice was signed, the KNCA said there was "nothing to talk to the puppet group of traitors about".
The hotline is used to facilitate the travel of South Korean workers to a joint industrial complex in Kaesong.
The hotline's 67 trained bilingual volunteers offer help in English, Spanish, Korean and Portuguese, New American Media reports.
Wary South Koreans are cancelling travel plans, staying away from hospitals and a MERS hotline is receiving thousands of calls.
North Korea has cancelled an armistice agreement with the United States that ended the Korean War (which technically never ended - there is no peace traty) and cut all hotlines with U.S. forces, the United Nations and South Korea.
