Ban said he had been briefed by his special envoy Ibrahim Gambari, who returned to New York this past weekend from a six-day visit in Burma aimed at convincing the military junta to agree to democratic reforms.
"As a result of this visit, a process has been launched that will hopefully lead to a meaningful and substantive dialogue with concrete outcomes within an agreed timeframe," Ban said in a statement.
"The secretary general welcomes the willingness expressed by both sides to work with the United Nations to this end," the statement said.
The president of the UN General Assembly, Srgjan Kerim, added his support to the reported agreement to start dialogue.
Kerim said he "welcomes the inauguration of a process that may lead to substantive and unconditional dialogue among the main parties."
He stressed the importance that this process must achieve "concrete results and a clear commitment" on the part of the government of Burma to work constructively with Gambari.
Both Ban and the UN Security Council have urged the Burma regime to move beyond the crisis in September when the military cracked down on demonstrations led by Buddhist monks, saying that a return to the pre-September period is not sustainable and acceptable.
They have called for democratic reform, national reconciliation, full respect of human rights in one of the world's poorest nations and the release of political prisoners, including Aung San Suu Kyi, leader of the opposition National League for Democracy.
UN Special Rapporteur Paulo Sergio Pinheiro arrived in Yangon Sunday to investigate the violent repression of the monks and their supporters during the September uprising.
The street demonstrations began after the government drastically increased prices of petrol in mid-August.
Gambari's visit last week was his second to Burma and he is scheduled to return there again for a third round of talks.
Ban said he wants Gambari to make an "early return to Burma as part of an open and regular process of mutual engagement."