The ruling party of South Korea's president said on Monday it wanted dialogue with North Korea over the shooting death of a South Korean tourist at a resort in the North to prevent already frayed ties from being further damaged.

North Korea rebuffed an olive branch extended last week by President Lee Myung-bak for talks, calling it "an intolerable insult," while analysts said the North is likely to stonewall attempts at dialogue to damage Lee, whose popularity has sunk due to policy blunders.

"I believe it is high time for the National Assembly to pioneer and spark dialogue," Hong Joon-pyo, a senior politician with the conservative Grand National Party, said in an address to parliament.

Hong pressed the North to cooperate in the investigation of the death of the woman, 53, who was gunned down by a North Korean soldier in the predawn hours of last Friday when she apparently wandered into a military area near the Mount Kumgang resort.

North Korea has blamed the South for the killing, refused to cooperate in a joint investigation and demanded an apology, which led to a furious reply from South Korea at the weekend.

"The act was wrong by any measure, unimaginable and should not have taken place at all," the Unification Ministry said.

South Korea suspended tours last week to Kumgang, which was hailed as a milestone in reconciliation between the states technically still at war when it opened in 1998. Nearly two million South Koreans have visited the resort located on the east coast just a few kilometres north of the heavily fortified border.

South Korea's largest daily, the Chosun Ilbo, said on Monday the killing may lead to the complete suspension of South Korean tourism to North Korea, which also results in the destitute North pocketing millions of dollars a year in fees paid by visitors.

"Inter-Korean ties are going to go down, definitely. But what happens thereafter depends largely on how this new government in Seoul follows through," said Lee Dong-bok, a senior associate in Seoul with the CSIS think tank.

"North Korea could have handled it in a way that would have brought a quick and rapid closing. Instead, North Korea has chosen to take advantage of it in their own way to mount pressure on the Lee Myung-bak government," Lee said.

President Lee has pledged massive assistance for his impoverished neighbour, but unlike his liberal predecessors who dispensed aid freely, has said Seoul's largesse would be tied to progress North Korea makes in nuclear disarmament.

North Korea, angered by that approach, branded Lee a "traitor to the nation" and said in April it was cutting off dialogue.

Ko Yu-hwan, a Dongguk University professor of North Korea studies, said cooler heads would eventually prevail because of economic and political interests shared by the states.

"If the confrontation reaches its peak, both sides will realise that they cannot go on like that," Ko said.

The shooting incident came as North Korea was meeting with five regional powers to discuss a disarmament-for-aid deal.

Analysts see the shooting issue as confined to the two Koreas for now and do not expect it to spill over to the international nuclear disarmament talks.

Meanwhile, the family of the shooting victim, Park Wang-ja, called on the North to come clean on the killing.

"I want all suspicions to be answered," her husband, Bang Yeong-min, a retired policeman, told the national daily JoongAng Ilbo. "I want the truth so that my wife can rest in peace.