Speaking to the U.N. Security Council, Ban urged Myanmar's military rulers to "take bold actions towards democratization and respect for human rights."
Ban spoke to the council just before his special envoy, Ibrahim Gambari, addressed members and spectators, including a dozen red-robed monks in the front row of the visitors gallery.
Gambari said the military government's new willingness to hold talks with detained opposition leader Aung San Suu Kyi marked "an hour of historic opportunity" after its deadly crackdown on pro-democracy protests.
Gambari, who returned earlier this week from the Southeast Asian nation, said he was "cautiously encouraged" that Myanmar's military ruler, Senior Gen. Than Shwe, is prepared to meet with Suu Kyi under certain conditions including giving up calls for international sanctions against Myanmar.
Suu Kyi has been detained for nearly 12 of the last 18 years and is currently under house arrest, although the government allowed her two brief meetings with Gambari during his four-day visit.
"The sooner such a meeting can take place, the better, as it is a first and necessary step to overcome the high level of mistrust between them," he said.
The government's conditions include giving up her calls for confronting the government and for imposing sanctions against it, Myanmar state media said.
"I sincerely hope that the potential for dialogue will be recognized to the same extent by both sides and that it can translate into concrete steps in the immediate wake of the crisis."
Gambari told the council that "another necessary step for genuine national dialogue to take place is the release of all political detainees, particularly the sick and the elderly."
Also Friday, the United States said a rare meeting in Myanmar between the country's deputy foreign minister and the acting U.S. ambassador there was not productive.
The ambassador, Shari Villarosa, told Myanmar that it must end its violent crackdown on peaceful demonstrators.
"It was not a terribly edifying meeting," said State Department spokesman Sean McCormack. "What she heard in private was not very different than what we hear from the government in public."
Villarosa, who has been a vocal critic of the crackdown, met with Deputy Foreign Minister Maung Myint in Naypyitaw, the regime's remote capital, about 240 miles north of Yangon, said a U.S. Embassy official, speaking on condition of anonymity, citing protocol.
Diplomats and opposition figures were skeptical that the junta's offer to meet with Suu Kyi was genuine but, nonetheless, have expressed hope that the meeting - something she has requested for years - would materialize.
The surprise move appeared aimed at staving off economic sanctions, thereby keeping Myanmar's bountiful natural resources on world markets, while also pleasing giant neighbor China, which worries the unrest could cause problems for the 2008 Beijing Olympics.
Many governments have urged stern U.N. Security Council action against Myanmar, but members China and Russia have ruled out any council action, saying the crisis does not threaten international peace and security.
"This issue does not belong to the Security Council," China's U.N. Ambassador Wang Gunagya said Thursday. "These problems still, we believe, are basically internal."
"No international imposed solution can help the situation," he added.
"Although action at the U.N. Security Council is unlikely because of China's opposition, the Council will hear a first-hand report from envoy Ibrahim Gambari in an open meeting, as well as in closed-door consultations, where more pressure is expected," says CBS News foreign affairs analyst Pamela Falk.
"China reversed course on its opposition to North Korea sanctions, and Council nations are expecting that increased pressure may do the same regarding Myanmar," Falk added.
State media in Myanmar gave new figures Thursday for the number of people arrested during last week's bloody assault by troops. The reports said nearly 2,100 people had been detained, with almost 700 already released.
The government has said 10 people were killed when security forces broke up the mass demonstrations, but dissident groups put the death toll at up to 200 and say 6,000 people were detained, including thousands of Buddhist monks who were leading the protests.