South Korea said the door remains open for face-to face-talks with North Korea, despite Pyongyang making their recent secret talks in Beijing public.

Earlier this week North Korea confirmed secret discussions between the two Koreas, still technically at war since the 1953 cease-fire that ended three years of brutal combat on the Korean Peninsula.

On Wednesday, North Korea's National Defense Commission said South Korean officials had "begged" to have several senior level meetings with North Korean government officials. But the commission now won't deal with South Korea, calling South Korean President Lee Myung-bak a "traitor" and threatening to cut off a military hotline in the east coast.

South Korean Foreign Ministry spokesman Cho Byung-jae said in a briefing that North Korea's threat to stop meeting "runs counter to the wishes of the international society and does not contribute to the peace and stability of the Korean Peninsula."

Cho said the "doors" to inter-Korean dialogue remain open. North Korea also should have a "responsible and sincere attitude" toward denuclearization -- a major issue that is destined to be part of any inter-Korean rapprochement.

South was forced to acknowledge the secret meeting with North Korean officials but denied it wanted a senior level summit meeting.

Confirmation of the meeting was made in the South Korean National Assembly by Seoul's Unification Minister Hyun In-taek.

The latest round of claims and counterclaims comes as relations between the two Koreas struggle to recover from more than a year of several serious military incidents that seriously worried Seoul's U.S. ally as well as China, one of the few countries to back Pyongyang.

Tensions rose dramatically between the two Koreas in November when the North unexpectedly shelled Yeonpyeong Island, killing two South Korean marines and two civilians. The South returned fire with 155mm K-9 self-propelled howitzers.

The shelling is believed to have been in response to South Korean military exercises in the politically sensitive sea area where the main Yeonpyeong Island is less than 8 miles from the North Korean mainland.

Yeonpyeong lies near the Northern Limit Line, the sea boundary agreed to by both Koreas in the 1953 armistice. But North Korea increasingly has contested the agreement in the past 15 years.

North Korea's National Defense Commission also continues to deny any involvement in the sinking in March 2010 of the South Korean navy's 1,200-ton patrol ship Cheonan in which 46 sailors died.

The blast was strong enough to break the ship in half. It had to be salvaged from the disputed shallow waters off the west coast near the 1953 demarcation line.

An international investigating team said it had found strong evidence that the Cheonan was sunk by a torpedo of North Korean manufacture and fired by a small to mid-size submarine.

Despite the war of words, North Korean leader Kim Jong Il, during his China visit last week, reportedly said he "advocates" an early resumption of the stalled talks among China, the two Koreas, Japan, the United States and Russia. The six-party talks covering North Korea's denuclearization were shelved in 2009 when Pyongyang pulled out to protest U.N. sanctions over its nuclear tests.

South Korea has maintained there can be no talks unless the North demonstrates its denuclearization commitment and takes responsibility for torpedoing of the Cheonan and shelling Yeonpyeong Island.