SEOUL, SEPT. 29 -- Korea's two top opposition leaders, after pledging to form a common front against the ruling party, today broke off talks on who should be the candidate, apparently paving the way for weeks of open competition and increasing the chances that both will run for president in December.

One day before their self-imposed deadline for reaching agreement, Kim Young Sam and Kim Dae Jung walked out of a two-hour meeting without an accord, promising only to meet again "if necessary."

"They apologize to the nation and the party for their failure to reach agreement," a spokesman said.

Kim Young Sam, who had pressed hardest for an early pact, suggested afterward that the failure could endanger the nation's progress from military rule to democracy. The progovernment Korea Times labeled the apparent breakup "disgusting." Many of the Kims' supporters said they feared that if both men run the opposition vote would be split, allowing the ruling party to win South Korea's first open election in 16 years.

But Kim Dae Jung, addressing a prayer meeting that turned into a campaign rally punctuated by cries of "Run! Run! Run!," said the split was temporary and simply represented democracy at work.

"If any political leader wants to run, first he must make his platform known to the people and so let the people choose," Kim said. "I think this is best for the principle of democracy."

President Chun Doo Hwan, who as a major general took power in a 1980 coup, has promised to step down in February, allowing the first peaceful transition of power in the republic's history.

But South Korea has seemed close to democracy before, which is why the nation has watched the two Kims' negotiations with painstaking interest. A similar competition between the longtime opposition leaders in 1980 was cited by the military as one destabilizing element that justified Chun's coup.

So when Chun, in response to widespread street protests, agreed July 1 to allow direct presidential elections, both Kims staked their reputations on a vow not to repeat their 1980 jousting.

But today each Kim argued openly for the first time that he should be the candidate. Supporters said both politicians now are likely to stage rallies across the nation, hoping to pressure the other to drop out.

"Their division will divide us all," one senior dissident leader of the National Council of Churches said. "The church group itself will be divided, friend against friend, it is unthinkable."

In their meeting today, the two Kims each found strengths in their very different images and histories: Kim Young Sam, the reassuring moderate who could ensure a stable transition, and Kim Dae Jung, the firebrand whose suffering under dictatorship gives him the moral authority to heal the nation.

Kim Young Sam's supporters have said that their man should run because the Army views Kim Dae Jung as a dangerous left-winger who should never be allowed to take power.

"It is reasonable for me to run. It is required for stability," Kim Young Sam said he told his rival in their meeting. "I did not talk about a veto group, but I told him that some people are worried about the possibility that he will take power."

Kim Dae Jung responded that in a democracy the military should not be allowed to determine who is a proper candidate.

"I will obey the people, not the military," he told his supporters. "If the people want me out, I will be out. But if the military wants me out, I will take it as one small piece of advice."

A ruling party strategist reacted cautiously to the dispute, saying the two Kims may still unite.

"At the last stage, they could come to a dramatic agreement, and then utilize that atmosphere of solidarity in the final days of the campaign," said Hyun Hong Choo.

Ruling party candidate Roh Tae Woo, an ally of President Chun, has his own problem: the probable candidacy of Kim Jong Pil, the "third Kim," a former prime minister who may take conservative votes from Roh. So analysts here now foresee a possible four-way contest.

The outcome of such a race is especially hard to predict because the government has banned publication of preference polls, or even informal straw polls. As a result, the city is swirling with rumors of polls privately conducted but not published.

One newspaper, for example, reportedly asked 1,500 potential voters whom they most respect in South Korea. Catholic Cardinal Stephen Kim topped the list, followed by Kim Dae Jung, Roh Tae Woo, Kim Jong Pil, dissident Rev. Moon I Kwan and Kim Young Sam, in that order.

But perhaps the most telling result was that barely one-third of those polled answered the question at all, a reflection of the dubious value of polling in a nation where the government has rarely tolerated a free expression of views.

The two opposition Kims started and jointly run the Reunification Democratic Party, but most members feel more loyalty to a personal faction than to the party. Still, a dozen RDP legislators today urged the two Kims to settle on one candidate.

"If both run and fail, there is no way we could show our face to the people," legislator Lee Chul said. "It would be committing a great sin."

Kim Dae Jung's supporters said they are convinced their man can win a four-way race. But Kim Young Sam said that if "four persons should run for president, military rule would not come to an end."

Kim Dae Jung responded that this year, unlike in 1980, democratic forces are strong enough "to keep the military at bay."