SEOUL, Aug 14 (Reuters) - North and South Korea delayed the start of their final day of high-level talks on Wednesday as aides battled to fix a date for crucial military meetings before issuing a joint statement.

South Korean Unification Minister Jeong Se-hyun and North Korean cabinet member Kim Ryong-song were to have begun their third day of talks at 9:00 a.m. (0000 GMT) at a hotel in Seoul.

Officials said aides had worked through the night on narrowing differences on when to hold military talks that are vital to an existing deal to restore a railway through the heavily fortified Demilitarised Zone (DMZ) that has bisected the peninsula since the end of the 1950-53 Korean War.

"The military meeting is the problem. They are still working on setting a date for the military talks. We are not sure when the last meeting will start," a Unification Ministry official told Reuters. "It's already lunch time."

Another ministry official made clear how much the outcome hinged on the dominant role of North Korea's armed forces.

"The North is waiting for word to arrive from their military," the official told Reuters. It was not clear what had been proposed.

The delegations had been scheduled to have lunch at 0300 GMT before the North Koreans headed back to Pyongyang.

South Korean officials say the sides have made headway, notably on family reunions and economic talks. The North has said it is optimistic about the outcome of the highest-level talks since the two navies clashed in disputed waters in June.

Forecasting the outcome of talks between the bitter rivals has always been risky. Promises made have often not been fulfilled, while optimistic assessments during the talks have on occasions degenerated into recriminations.

Tuesday's talks focused on how to revive a plan to reconnect a railway across one of the world's most dangerous borders, and how to reunite families split for half a century.

WASHINGTON WATCHING

South Korean media said it was possible a temporary reunion of some families could be held at the North's Mount Kumgang resort around the September 21 Chusok national holiday.

The most recent reunions -- when family members meet for a few days and then part again -- took place in April and May.

South Korean media also said economic talks could be held this month and Red Cross talks in early September.

One issue that has not been discussed in Seoul was the fate of thousands of North Korean refugees in northeastern China and the many asylum seekers who have entered foreign embassies in Beijing. Two North Koreans climbed a fence into the Albanian embassy on Tuesday and asked to go to the South.

So far this year China has allowed scores of asylum seekers to leave for Seoul, but through a third country to avoid offending its Communist ally, which is technically still at war with the South.

The United States and Japan, and other regional players, have been monitoring the North-South talks to see whether Pyongyang's recent burst of diplomatic activity will be translated into action.

There were fresh signs on Tuesday of just how volatile diplomacy can be on the Korean peninsula. As the teams negotiated at a Seoul hotel, the North Korean Foreign Ministry in Pyongyang denounced the United States and threatened to pull out of a crucial nuclear agreement.

Harsh statements in the past have proved to be pre-negotiation bluster, and U.S. officials tend to view them as a sign Pyongyang is gearing up for serious exchanges.

North Korea held military talks with officers from the U.S.-led United Nations Command on Tuesday at the truce village of Panmunjom in the DMZ to discuss the June naval clash in which five South Korean sailors died. The South estimates up to 30 North Koreans were killed or wounded.

At an unprecedented summit two years ago, South Korean President Kim Dae-jung and North Korean leader Kim Jong-il agreed to rebuild the rail line.

The South has completed its railway and a parallel road right up to the edge of the DMZ, but the North has done little.

President Kim, 77 and in the final months of his five-year single term, was resting with pneumonia. His office said he would not deliver a speech on Thursday, the anniversary of the end of Japanese colonial rule in 1945.

Kim won the Nobel Peace Prize in 2000 for his "Sunshine Policy" efforts to engage the North and is eager to show a sceptical South Korean public some tangible results ahead of a presidential election in December. Kim cannot stand again, but his party's chosen candidate is trailing in opinion polls.

A civic delegation from the North arrived in South Korea on Wednesday to take part in events to mark independence day. Nampa-Reuters 0545 140802 WEB story ENDS (NAMPA 140549)