"They strongly urged Myanmar to exercise utmost restraint and seek a political solution," the statement said and urged Myanmar to release political detainees including democracy activist Aung San Suu Kyi.
Gambari, a Nigerian U.N. undersecretary-general, is now in Myanmar's eastern neighbor, Thailand, awaiting a visa.
A U.N. spokeswoman said Ban urged the authorities in the former Burma "to engage in a constructive dialogue with his special adviser and to commit to a path of peaceful and inclusive national reconciliation".
U.S. Ambassador to the United Nations Zalmay Khalilzad told reporters it was important that Gambari be allowed to meet "all the relevant people", including opposition figures such as Aung San Suu Kyi.
A report by Gambari, particularly a negative one, would keep the issue before the U.N. Security Council. China and Russia, which have friendly ties with the Myanmar authorities, in January vetoed a U.S.-drafted resolution calling on the junta to stop persecution of minority and opposition groups.
A senior Western diplomat said the Gambari mission gave the Myanmar authorities a "face-saving vehicle" for starting a political process of dialogue with the opposition if they chose to use it. A refusal to receive him would have sent a clear message of the junta's intentions.
British Foreign Secretary David Miliband said sending Gambari "reinforces the idea that the world is watching".
Thursday's ASEAN statement made no mention of sanctions or other punitive measures against the military government that has ruled the former Burma in various forms since 1962.
The ministers, who met U.S. Secretary of State Condoleezza Rice on Thursday, said the carnage in Myanmar had "a serious impact on the reputation and credibility of ASEAN."
Southeast Asia's main diplomatic and trade grouping consists of Indonesia, Malaysia, Philippines, Singapore, Brunei, Vietnam, Laos, Thailand, Myanmar and Cambodia. Myanmar joined ASEAN in 1997 amid controversy over its repressive government.
