North Korea has threatened to use force to stop the broadcasts, ratcheting up tensions on the Korean Peninsula.
High-level talks to resolve the issue went through a second night on August 23.
Both Korea’s militaries are on alert after a brief exchange of fire at the border on August 20.
North Korea denies laying the landmines which maimed the soldiers earlier this month as they were patrolling the Demilitarized Zone (DMZ), the heavily fortified border.
It also denies shelling South Korea on August 20, an incident which prompted return artillery fire from the South.
“We need a clear apology and measures to prevent a recurrence of these provocations and tense situations,” said President Park Geun-hye according to a statement released by her office.
“Otherwise, this government will take appropriate steps and continue loudspeaker broadcasts.”
South Korea resumed the propaganda broadcasts along the DMZ earlier this month, after an 11-year hiatus, in apparent retaliation for the landmine attack.
The talks that began on August 22 in the abandoned “truce village” of Panmunjom inside the DMZ have, for the time being, subdued heated rhetoric of imminent war.
South Korea is represented by national security adviser Kim Kwan-jin and Unification Minister Hong Yong-pyo, while the North has sent senior officials Kim Yong-gon and Hwang Pyong-so, who is seen by many analysts as North Korean leader Kim Jong-un’s second-in-command.
However, South Korea’s military had said that most of North Korea’s submarines appeared to be away from their bases, and amphibious landing vessels had been deployed to the border, the Yonhap news agency reports.
On August 21, North Korea ordered its troops to be “on a war footing”.
South Korea has evacuated almost 4,000 residents from border areas and warned that it would “retaliate harshly” to any acts of aggression.
In 2004, the two Koreas reached an agreement to dismantle their propaganda loudspeakers at the border.
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