North Korean leader Kim Jong-Il believes his communist regime is "invulnerable", state media said Sunday, as tensions mounted over a planned rocket launch and a border closure.

Kim made the remark as he watched one of his artillery units perform a live-fire exercise, the Korean Central News Agency (KCNA) said, failing to give a date or location for when Kim made the comments.

"Our socialist fortress is invulnerable and our revolutionary cause is sure to win one victory after another as we have these steel-like elite ranks," Kim said, according to KCNA.

The communist state last week notified international aviation and maritime agencies that it would launch a communications satellite April 4-8.

Seoul and Washington say the launch is a pretext to test its Taepodong-2 missile -- the first one technically capable of reaching North America. It would be the third long-range missile test since 1998.

The North on Monday switched off military phone and fax lines, used to approve border crossings with the South, and put its 1.2-million-member army on combat alert to protest an ongoing annual US-South Korean military exercise.

It says the exercise involving tens of thousands of troops is aimed at launching a "second Korean War," while Seoul and its ally Washington insist it is a routine annual defensive drill.

The border with the South remained shut for a third consecutive day Sunday, stranding hundreds of South Koreans in the North.

Seoul's Unification Minister Hyun In-Taek urged Pyongyang to allow businessmen and investors to travel freely to and from the South Korea-funded industrial site in Kaesong, just north of the border.

"North Korea's unilateral and unfair action like this not only undermines inter-Korean accords but also violates its own regulations," Hyun said Sunday at a meeting with southern businessmen.

A group of 72 South Korean businesses operating in Kaesong warned that their production would come to a halt due to a lack of raw material unless the crossings resume in a week.

Seoul's unification ministry has reported that 427 people were not allowed to return home from Kaesong on Friday and Saturday.