STORY HIGHLIGHTS
- NEW: Seoul is signaling to Pyongyang it could shut down the complex, an analyst says
- South Korea calls on North to respond to offer of talks by noon on Friday
- It warns of "grave" measures regarding the zone if Pyongyang rejects the offer
- North Korea suspended activity at the joint industrial zone this month
Seoul, South Korea (CNN) -- South Korea on Thursday warned North Korea of serious consequences if it rejects an offer for talks about the dire situation at their shared manufacturing zone where Pyongyang has halted activity amid recent tensions.
The South Korean Unification Ministry spokesman Kim Hyung-seok urged the North to respond to the offer of talks by noon Friday, saying South Koreans inside the zone, the Kaesong Industrial Complex, are facing "serious difficulties due to lack of food and medical supplies."
Kim said that if Pyongyang turns down the offer, Seoul would have no choice but to take "grave" measures regarding the zone. He did not specify what those measures would be.
Seen as the last major symbol of cooperation between the two countries, the Kaesong complex is a joint economic zone on the North's side of the border that houses the operations of more than 120 South Korean companies.
Earlier this month, during a frenzy of fiery rhetoric directed at South Korea and the United States, the North began blocking South Koreans from entering the complex across the heavily fortified border.

Emergency service personnel wearing chemical protective clothing participate in an anti-chemical warfare exercise on Tuesday, April 16 in Seoul. Tensions remain high in the Korean Peninsula in the wake of North Korea's recent nuclear threats and provocations. A Pentagon intelligence assessment suggests the North may have the ability to deliver a nuclear weapon with a ballistic missile, though the reliability is believed to be "low."
South Korean marines arrive on the island of Yeonpyeong near the disputed waters of the Yellow Sea on Friday, April 12.
A Japanese soldier is on alert as Patriot Advanced Capability-3 missile launchers are deployed at the Defense Ministry in Tokyo on Wednesday, April 10.
South Korean soldiers sit in a truck at the Inter-Korean transit office on Tuesday, April 9, in Paju, South Korea.
South Korean soldiers participate in an artillery drill as part of the Foal Eagle joint military exercise by U.S. and South Korean forces near the Demilitarized Zone in Goseong on April 9.
U.S. soldiers are at a military training field in Yeoncheon, South Korea, on April 9.
South Korean soldiers with K-55 self-propelled Howitzers stage at a military training field in the border city of Paju on Friday, April 5, as tensions continue to mount on the Korean peninsula.
South Korean soldiers man a cannon at a military training field in Paju on April 5.
South Korean soldiers stand guard at a sentry post at the border with North Korea in the Demilitarized Zone near Imjingak, South Korea, on April 5.
A U.S. Army Patriot missile battery is visible at the U.S. Osan Air Base in South Korea on Friday, April 5.
The U.S. Navy is moving a sea-based radar platform, like the one seen in this 2006 file photo, closer to the North Korean coast to monitor that country's military moves, including possible new missile launches, a Defense Department official said Monday, April 1.
South Korean marines man K-55 self-propelled Howitzers at a military training field in the border city of Paju on Monday, April 1. Park Geun-hye, South Korea's new president, promised a strong military response to any North Korean provocation after North Korea announced that the two countries were in a state of war.
South Korean anti-aircraft armored vehicles move across a temporary bridge during a river crossing drill in Hwacheon near the North Korean border on Monday, April 1.
South Korean soldiers ride on a military truck in Paju on Friday, March 29.
The United States said Thursday, March 28, that it flew stealth bombers over South Korea to participate in annual military exercises amid spiking tensions with North Korea. Pictured, a B-2 Spirit stealth bomber flies over South Korea's western port city of Pyeongtaek.
South Korean soldiers gather at the foot of a mountain near a military drill field in the border city of Paju on Wednesday, March 27.
Armed South Korean soldiers walk on a road near a military drill field in Paju on March 27.
South Korean soldiers ride in a military truck in Paju on March 27.
A B-52 bomber flies over the wire-topped fence of a U.S. air base in Osan, South Korea, on Tuesday, March 19.
South Korean soldiers take part in a drill to guard the building of a state-run telecom company in Seoul against potential guerrilla attacks on Thursday, March 14.
South Korean army soldiers jump off a military truck during a drill outside a U.S. airbase in Pyeongtaek as part of annual joint exercises with the United States on March 14.
South Korean Marines operate K-55 self-propelled howitzers on the western island of Ganghwa near the disputed maritime frontier with North Korea on Wednesday, March 13.
South Korean soldiers stand guard as a North Korean soldier, far center, looks on at the truce village of Panmunjom in the demilitarized zone dividing the two Koreas on March 13.
South Korean marines patrol on the South Korea-controlled island of Yeonpyeong near the disputed waters of the Yellow Sea on Tuesday, March 12.
In this Navy handout image taken on March 5, Lt. j.g. Matthew Harmon serves as helm safety officer aboard the guided-missile destroyer USS McCampbell during a replenishment at sea, part of Foal Eagle 2013, the joint exercises between the United States and South Korea.
Fire Controlman 2nd Class Jason Titcombe, left, hands Fire Controlman 2nd Class Joshua Clements ordnance aboard the destroyer USS Lassen in this Navy handout photo taken on March 5.
U.S. Navy Boatswain's Mate 3rd Class Brittany Chiles signals to an SH-60B Seahawk helicopter as it lands on the flight deck of the destroyer USS McCampbell on March 4 in the Pacific Ocean, in this Navy handout photo.
This March 17 Navy handout image shows the destroyer USS John S. McCain, front; the Republic of Korea Navy destroyer ROKS Seoae-Yu-Seong-Ryong, center; and the destroyer USS McCampbell moving into formation in the waters off the Korean Peninsula during exercise Foal Eagle 2013.
Militaries and Korean tensions
Militaries and Korean tensions
Militaries and Korean tensions
Militaries and Korean tensions
Militaries and Korean tensions
Militaries and Korean tensions
Militaries and Korean tensions
Militaries and Korean tensions
Militaries and Korean tensions
Militaries and Korean tensions
Militaries and Korean tensions
Militaries and Korean tensions
Militaries and Korean tensions
Militaries and Korean tensions
Militaries and Korean tensions
Militaries and Korean tensions
Militaries and Korean tensions
Militaries and Korean tensions
Militaries and Korean tensions
Militaries and Korean tensions
Militaries and Korean tensions
Militaries and Korean tensions
Militaries and Korean tensions
Militaries and Korean tensions
Militaries and Korean tensions
Militaries and Korean tensions
Militaries and Korean tensions
Militaries and Korean tensions
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Photos: Militaries and Korean tensions
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North Korea's reluctance to talk
It then pulled out the more than 50,000 North Koreans who work in the zone's factories, saying it was temporarily suspending activity there. The move surprised some observers, since Kaesong was considered to be a key source of hard currency for the regime of Kim Jong Un.
The production halt was one of the most tangible signs of the heightened tensions on the Korean Peninsula in the past few weeks. The situation had deteriorated after the North carried out its latest underground nuclear test in February, prompting the U.N. Security Council to tighten sanctions on the regime in Pyongyang.
The tougher sanctions, together with joint U.S.-South Korean military training exercises in South Korea, generated an intensification in North Korea's threats against Washington and Seoul.
The North's fiery rhetoric, which unnerved the United States enough for it to move missile-defense systems into the region, has since appeared to calm somewhat. And the U.S.-South Korean military exercises are due to end in the coming days.
But the situation at the Kaesong complex remains up in the air.
Some South Koreans, who manage the factories in the zone, have remained inside since the North started preventing people from entering from across the border. If they leave, they don't know when they'll be allowed back in.
The number of non-North Koreans in the complex has steadily dwindled from more than 800 before the crisis began. As of Wednesday, 176 South Koreans and one Chinese person remained in the Kaesong complex, according to South Korean authorities.
Citing the difficulties experienced by those still inside the zone and the harm the situation is doing to the companies involved, Kim, the Unification Ministry spokesman, said Thursday that the complex couldn't be left as it is.
He said the talks South Korea is proposing would aim to "resolve the humanitarian problem" of those still inside the zone and to normalize operation of the factories.
"South Korea is signaling to the North that they are willing to consider the option of shutting down the Kaesong Industrial Complex," said Jasper Kim, founder of the Asia-Pacific Global Research Group in Seoul. "But in all likelihood that is not what it wants."
He said that although the economic cost of closing the complex would hurt the North more than the South, Seoul is more likely to be concerned about the political consequences of bringing an end to the symbol of cooperation.
There didn't appear to be an immediate reaction from North Korea on its state-run Korean Central News Agency.
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CNN's K.J. Kwon reported from Seoul, and Jethro Mullen reported and wrote from Hong Kong.