South Korean troops closed in Monday on a cornered fugitive conscript whose parents urged him to surrender after he killed five fellow soldiers in a shooting spree on the border with North Korea.

Thousands of soldiers backed by special forces units and army helicopters were surrounding the 22-year-old sergeant after a night-long standoff in a small forested area south of the heavily militarised frontier.

"We are closing in on him and he was close enough to be able to pick up a cell phone we threw," defence ministry spokesman Kim Min-Seok told a briefing.

Kim said the sergeant, identified by his family name Lim, had spoken to his father who had urged his son to give himself up.

An army officer who requested anonymity told Yonhap news agency that Lim had been in tears when he asked troops to hand the phone over to his father. "He talked to his parents for several minutes, and they pleaded with him to surrender," the officer was quoted as saying.

Lim, who had not eaten for two days, was also thrown some bread and water.

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.

He traded fire with his pursuers late Sunday before digging in for the night in a section of forest outside a village some 10 kilometres (six miles) away.

Kim said there were further sporadic exchanges of fire during the night, and Lim was still considered extremely dangerous.

"We don't plan to immediately move to capture him because we don't want to trigger any extreme behaviour," he said.

"We are encouraging him to surrender," he added.

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.

The incident triggered a massive military manhunt involving more than 4,000 soldiers, including special forces backed by army helicopters.

After a night on the run, Lim was finally cornered near Myungpa-ri village in eastern Gangwon province.

In the initial exchanges of fire one platoon leader was wounded in the arm, and Kim said another soldier was wounded Monday by friendly fire.

Around 500 residents, most of them elderly, were evacuated from their homes to a school building as a precaution.

- Bullying in the barracks -

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.

Because the 1950-53 Korean War ended with a ceasefire rather than a peace treaty, the two Koreas technically remain at war.

Many of the South Korean soldiers on border duty are young male recruits doing their mandatory two-year military service.

These young men make up a large part of the South's 691,000-strong troop presence, compared with 1.17 million in the North.

Most of the victims in Saturday's shooting were conscripts, aged from 19 to 23.

The defence ministry issued a "sincere apology" over the incident.

"We pray for the souls of the victims and express our deepest regret for the victims, the injured and their families," it said.

Bullying and cruelty in the barracks have long tarnished the armed forces, and been blamed for suicides and similar shooting incidents.

In July 2011, a 19-year-old marine conscript killed four colleagues in a shooting spree on Ganghwa island near the border.

In June 2005, eight soldiers were killed and two seriously wounded when a 22-year-old conscript threw a grenade and sprayed bullets over sleeping colleagues at a frontline guard post north of Seoul.