Initial media reports that the 23-year-old sergeant had been captured after a standoff with thousands of soldiers overnight were denied by the defence ministry, which said it was still hoping he could be persuaded to give himself up.
Officials refused to confirm television news channels that the soldier, identified by his family name Lim, had been speaking to his father and was preparing to surrender.
Armed with a K-2 assault rifle and a stash of ammunition, Lim went on the run Saturday night after killing five fellow soldiers at a frontline border outpost.
"Our goal is still to capture him alive," a senior military official told AFP.
Seven others were wounded in Lim's shooting spree on Saturday, during which he detonated a grenade and fired multiple rounds.
Lim was due to be discharged in the next few months after completing his compulsory military service.
The motive behind the shooting was unclear, but army sources said he had difficulty adapting to the military, and psychological evaluators had advised senior officers to pay him special attention.
After a night on the run, Lim was finally cornered 10 kilometres (six miles) away, near Myungpa-ri village in eastern Gangwon province.
There were several exchanges of fire on Saturday night, during which one platoon leader was shot and wounded in the arm.
Around 500 residents, most of them elderly, were evacuated from their homes to a school building as a precaution.
Lim's deadly shooting spree occurred at a guard post next to the Demilitarised Zone (DMZ) -- a buffer strip that runs the full length of the 250-kilometre (155-mile) inter-Korean frontier.