Media playback is unsupported on your device Media caption "This really is the first key test of relations between the two countries"

South Korea's former First Lady has travelled to Pyongyang to offer condolences over Kim Jong-il's death.

Lee Hee-ho, whose husband Kim Dae-jung tried to improve relations with the North, is the highest-profile of two delegations allowed by the South.

Officials said Mrs Lee, 89, was not representing the government. She will not stay for the funeral on Wednesday.

Meanwhile, state media in the North continues to promote Kim Jong-il's son, Kim Jong-un, as his father's successor.

The Rodong Sinmun newspaper has described Kim Jong-un as the head of the Workers' Party Central Committee, meaning that he now controls one of the country's highest decision-making bodies.

The newspaper earlier gave him the title of "supreme commander" of the armed forces.

Clinging to power

Seoul has allowed only two private delegations to travel north to pay their respects, and will not be sending any officials to the funeral.

The South's refusal to allow its citizens to travel has angered Pyongyang, which has warned of "grave implications" for relations.

Mrs Lee, who met Kim Jong-il during a landmark summit in 2000, said in a statement that she hoped her visit would help to improve relations on the peninsula.

Analysis When Kim il-Sung died in 1994, South Korea didn't send any kind of condolence message and didn't allow people to travel north. That created a lot of bad blood between the two countries. At the moment South Korea says it is keen to not appear hostile. The president has said he wants to try to reach out, and the government has sent a message of sympathy to the North Korean people. As far as the North Korean media sees it, this gesture is not enough. They say it is the first real test of relations between the two countries during the mourning period, and the South has failed.

"As chairman Kim Jong-il sent a condolence delegation to Seoul when my husband passed away in 2009, I believe it is our duty to express our condolences," she said.

Kim Dae-jung pioneered what became known as the Sunshine Policy, trying to engage the North through diplomacy.

However, the current government ditched the policy in 2008 and has since taken a tougher line towards the nuclear-armed North.

Mrs Lee travelled overland to Pyongyang, where she is expected to stay for two days.

The chairwoman of the Hyundai firm, Hyun Jung-eun, is also visiting Pyongyang to offer condolences.

Her company was at the forefront of efforts to build business ties with the North, and Kim Jong-il also sent condolences when her husband died.

Crowds of mourners continued to pour into Pyongyang's Kim il-Sung square on Monday.

A vast portrait of Kim Jong-il is hanging in the square, and North Koreans gathered in orderly lines in front of the picture to express their condolences.

Some were overcome with grief and burst into tears, in now familiar scenes broadcast by state media since Kim Jong-il's death on 17 December.

North Korea is trying to carry on the world's only Communist family dynasty.

Kim Jong-il inherited power from his father Kim il-Sung in 1994 after more than two decades being primed for the role.

However, his son Kim Jong-un is still in his 20s and has very little political experience.

Analysts say he will be surrounded by a group of experienced military insiders and relatives, as the Pyongyang elite attempts to hold on to power.