SEOUL - North Korea on Saturday threatened to shut down a joint industrial complex with South Korea, state media said, in the latest warning from Pyongyang at a time of escalated tensions between the two sides.

The threat from the state body in charge of the complex just north of the Korean border followed an announcement by the North on Wednesday that it was cutting its last military hotline with the South.

"We will relentlessly close the industrial complex if South Korea tries to damage our dignity even a little," the body said in a statement carried by the North's official Korean Central News Agency.

"We warn that stern measures will be taken if (South Korea) continues to make reckless remarks defaming our dignity," it said, adding the fate of the complex depends "entirely" on the attitude of Seoul.

The industrial complex which lies 10 kilometres inside North Korea was established in 2004 as a symbol of cross-border cooperation.

North Korea has always been wary of allowing crises in inter-Korean relations to affect the zone - a crucial hard-currency earner for the communist state.

But there have been concerns that operations at the complex would be affected by Pyongyang's move to sever the military hotline used to monitor movement in and out of the zone.

The line was used daily to provide the North with the names of those seeking entry to Kaesong, guaranteeing their safety as they crossed one of the world's most heavily militarised borders.

Earlier on Saturday, North Korea declared it was in a "state of war" with South Korea and warned Seoul and Washington that any provocation would swiftly escalate into an all-out nuclear conflict.

It was one of several dire-sounding pronouncements from Pyongyang recently that have been matched by tough warnings from Seoul and Washington, fuelling international concern that the situation might spiral out of control.