Ministry spokesman Cho Tai-young said terms of the agreement "cannot be unilaterally invalid or terminated" and demanded North Korea withdraw its threats, Yonhap reported.
North Korea declared the cease-fire "completely invalid" in response to a fourth round of U.N. sanctions against the country for its third nuclear test and in reaction to the annual joint military drills between South Korea and the United States.
North Korea also threatened to launch pre-emptive nuclear strikes against South Korea and the United States, as well as other actions, because of the new sanctions and the drills.
Cho said South Korea will "strengthen coordination and cooperation with the U.S. and China, and sternly deal with any attempt from North Korea to scrap the Armistice Agreement."
U.N. spokesman Martin Nesirky also said North Korea could not dissolve the armistice unilaterally, The New York Times reported.
Kim Min-seok, a South Korean Defense Ministry spokesman, said Tuesday nothing signaled an imminent nuclear or missile test by North Korea or hostilities along the Korean border.
He said the "rhetorical threats" presented by North Korea's state-run media were meant to exert "psychological pressure" on South Korea, the Times said.
"Through a series of political and military activities, North Korea is strengthening the solidarity of its people at home while using the [military] exercises as a pretext to threaten and pressure South Korea and the United States to change their polices," he said. "If they launch a provocation, we will respond more strongly and make sure that they suffer far more."