The leader of South Korea's ruling Grand National Party has proposed dialogue with North Korea to reduce tensions caused by the shooting death last week of a South Korean tourist by a soldier.

Floor leader Hong Joon-pyo told parliament in Seoul today that the communist North also should cooperate in an investigation into the death last week of the 53-year-old housewife.

Seoul's Unification ministry said in a statement Sunday that if Pyongyang does not allow South Korean authorities to investigate the incident, it would have serious consequences for North-South relations.

A statement from Pyongyang said no South Korean investigators will be allowed to look into the circumstances of the shooting.

North Korea has said it regrets the tourist's death, but that South Korea was at fault and should apologize.  

The tourist was killed when she walked into a restricted beach area guarded by the North Korean military.   The woman had been vacationing at the North's nearby Kumgang mountain resort.

South Korea built the resort and funds it as a showcase of improved North-South relations.  After the shooting, all tours were suspended and South Korean vacationers returned home.

On the same day as the shooting, South Korean President Lee Myung-bak had called for the resumption of reconciliation talks with North Korea.  

Pyongyang has rejected the call for renewed dialogue, calling President Lee a "traitor" for taking a more conservative policy line on the North than his two predecessors.

North and South Korea technically remain at war, with only a 1953 armistice sustaining a tense peace along their border.

Some information for this report was provided by AP and Reuters.