Soe Win had been hospitalised in Singapore since March, reportedly for leukaemia treatments, but is believed to have returned to Yangon in recent weeks.
Soe already handed over his duties in May to Lieutenant General Thein Sein, who ranks fifth in the military leadershup, and who has been referred to as acting prime minister in state media.Soe Win's death was not expected to have a major impact on the government because all real power lies with Senior General Than Shwe and the military leaders.
Selina Downes, Al Jazeera's correspondent in Bangkok, says that Soe Win was thought not to have been involved in the recent violent crackdown on pro-democracy demonstrators but had a key role in the suppression of protests in 1988 that left thousands dead.
The announcement of Soe Win's death came as the military regime expressed its regret at a statement issued by the UN security council deploring the violent crackdown on the peaceful pro-democracy protests last month.
"Myanmar regrets that the statement by the chairman of the UN Security Council was announced on October 11, although [the] situation in the Union of Myanmar did not harm regional or international peace and security," state television said.
The statement said: "The Security Council strongly deplores the use of violence against peaceful demonstrations in Myanmar ... [and] emphasises the importance of the early release of all political prisoners and remaining detainees."
"Where are the peace and human rights defenders of the world (the super powers)? They haven't done enough in this case. Isn't there oil in Myanmar?"
Lost Soldier, Arusha, Tanzania
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It is the first time the council has taken any action over Myanmar and marks a shift of position by China, which had previously used its veto to stop the 15-nation body from voicing criticism of Myanmar's military government.
The statement called on Myanmar and all other parties concerned to work together towards a de-escalation of the situation and a peaceful solution.
It also said the Myanmar government should "create the necessary conditions for a genuine dialogue with Daw Aung San Suu Kyi [the democracy leader] and all concerned parties and ethnic groups in order to achieve an inclusive national reconciliation".
Aung San Suu Kyi's National League for Democracy welcomed the security council statement.
"Since Myanmar is a member country of the United Nations and as the government has declared it would work with the UN, we earnestly underscore the need to urgently implement the demands made by the Security Council," the statement said.
Meanwhile, the UN said Ibrahim Gambari, its special envoy to Myanmar, would set off over the weekend for a tour of Asia.
The trip is expected to culminate in what would be the envoy's second visit to Myanmar since the demonstrations erupted.
The US however wants Gambari to head directly to Myanmar instead of visiting other Southeast Asian nations first.
"Given the continuing abuses of the junta on Burma, we urge UN Special Advisor Gambari to return to Burma as soon as possible," Tony Fratto, a spokesman for the White House, said, using Myanmar's former name."We would like to see advisor Gambari visit Burma before he visits other regional capitals."