Anutin made the remarks after meeting ASEAN Secretary-General Kao Kim Hourn, a day after holding talks with Indonesian President Prabowo Subianto.
Myanmar has been in turmoil since February 2021, when the military, led by Min Aung Hlaing, overthrew the elected government of Nobel Peace Prize laureate Aung San Suu Kyi. The coup triggered nationwide protests that evolved into a prolonged civil war, killing an estimated 100,000 people and displacing millions.
In response, ASEAN barred Myanmar's top leaders from attending its high-level political summits.
In a policy speech, Anutin said ASEAN's peace roadmap for Myanmar, known as the Five-Point Consensus, remains the bloc's guiding framework for addressing the crisis. The plan calls for an immediate cessation of violence, inclusive dialogue among all parties and the delivery of humanitarian assistance.
"Thailand has advocated a calibrated re-engagement approach that keeps dialogue open and responds to realities on the ground while encouraging concrete progress," he said.
Anutin said the approach appeared to be yielding results, pointing to Aung San Suu Kyi's meeting on Monday with a representative of the International Committee of the Red Cross, her first publicly known meeting with a foreign official since the coup. He said she appeared to be in good health.
"This has been what Thailand has advocated all along," he added.
Anutin is scheduled to meet Min Aung Hlaing in Thailand on August 6 and 7.
He said ASEAN's long-standing principle of non-interference remains fundamental but should be applied with the flexibility and pragmatism needed to preserve the bloc's unity.
Analysts have warned that ASEAN's renewed engagement with Myanmar risks conferring legitimacy on the military-backed government.
Last month, Philippine Foreign Minister Maria Theresa Lazaro said Myanmar's full participation in ASEAN meetings remained "still far off".
Min Aung Hlaing became Myanmar's president in April after military-engineered elections that human rights groups and Western governments dismissed as a "sham".