Al Jazeera's Marga Ortigas reported from Singapore: "They believe this is the best way forward in terms of working with the Myanmar government and assuring that the aid gets through."
She said: "All efforts be it from the US or other western nations - all efforts from outside the region - will have to go through Asean."
The military government later declared a three day period of mourning for cyclone victims.
World powers have tried for weeks to get Myanmar's rulers to allow foreign aid workers into Myanmar, but restrictions imposed by the country's ruling generals have hampered relief efforts.
John Holmes, the UN relief co-ordinator, was shown round the Myanmar's cyclone-hit area on Monday, and delivered a letter from Ban Ki-moon, the UN secretary-general, to Myanmar's military leaders.
Ban, due to visit the country on Thursday, was unable to get Than Shwe, Myanmar's senior general, to even accept his telephone calls in the aftermath of Cyclone Nargis, which has left at least 133,000 people dead or missing.
Than Shwe made his first public appearance since the disaster, shown on state television in Yangon on Monday.
The reclusive leader was shown inspecting water supplied for cyclone-victims and meeting ministers involved in the relief operations.
The UN believes 2.4 million people are still short of aid 17 days after the tragedy struck.
Relief agencies have warned that the most vulnerable survivors will start dying soon unless they get the aid they need.
The UN has said only a fraction of the emergency supplies needed have got through to people in the Irrawaddy Delta, where whole villages were swept away when Cyclone Nargis hit on May 2-3.
"This is not of the quantity or frequency required to meet the needs of the affected populations," it said in its daily update, adding that hungry survivors were migrating out of their villages in search of food.
"The need is still overwhelming the actual relief response," Chris Webster, a spokesman for aid group World Vision, said in neighbouring Thailand.
"There's a huge challenge in the hands of the aid workers and we don't have all the people we need [in Myanmar]."
Among other delays, Myanmar has not yet granted visas to dozens of disaster relief specialists, while US and French ships carrying aid remain without clearance to come into port.
Prior to the Asean talks, Myanmar's rulers proposed a donor conference be held in Yangon, one of its main cities and which was hit by the cyclone.
"We have to listen to Myanmar's opinion first," Noppadon Pattama, the Thai foreign minister, said.
Ministers at the Asean talks in Singapore observed a minute's silence in remembrance of the victims of Asia's twin tragedies this month - the Myanmar cyclone and last week's devastating earthquake in China.