A spokesman for the North Korean department controlling Kaesong was quoted by the state news agency as warning the country would "shut down the zone without mercy" if it felt it was not being taken seriously.
Recent weeks have seen a torrent of bellicose rhetoric from Pyongyang threatening dire consequences for both South Korea and the United States. North Korea is angry about the annual South Korea-US military drills, which will run until the end of this month, and at the UN sanctions imposed after it carried out another nuclear test in February.
North Korea is also seen as trying to persuade the new Government in Seoul, led by President Park Geun Hye, to change its policies towards Pyongyang, and also to win diplomatic talks with the US that could get it more aid.
A final factor could be a attempt by the North's young leader, Kim Jong Un, to build a sense of unity in the secretive state by highlighting a sense of an outside threat.
Though the two Koreas have technically been at war for more than half a century - having never signed a formal peace deal after the Korean War in the 1950s - there is a concern that mis-steps could provoke a real crisis.
On Friday, US military officials revealed that two B-2 stealth bombers dropped dummy munitions on front lines as part of their drills with South Korean troops. Hours later, Kim ordered his generals to put rockets on standby and threatened to strike US targets if provoked.
But generally North Korea watchers and senior security officials in the White House and the Pentagon have sought to play down the crisis, portraying it as just the latest in a long series of such incidents.
Yesterday National Security Council spokeswoman Caitlin Hayden said the US was in close contact with Seoul and took the threats seriously.
But she added that North Korea had repeatedly made such threats, including claims it would shut down Kaesong.
"North Korea has a long history of bellicose rhetoric and threats and today's announcement follows that familiar pattern," she said.
That was backed up by top White House officials. CBS news reported that a senior member of President Barack Obama's Administration had played down any prospect of actual hostilities. "North Korea is in a mindset of war, but North Korea is not going to war," the official told the TV station.
But, despite such attempts at maintaining calm, the US has also strengthened its missile defence capabilities on its west coast.
"We continue to take additional measures against the North Korean threat," Hayden added, "including our plan to increase the US ground-based interceptors and early warning and tracking radar."
- Observer