Modi was received by Filipino President Rodrigo Duterte at the ceremony here.
Ballet company Rama Hari presented the Filipino version of the Ramayana which is known as 'Maharadia Lawana', meaning King Ravana.
It is the Maranao version, which refers to the people living around Lake Lanao in the Philippines.
"You would be happy to know that the @ASEAN opening ceremony included excerpts from the musical Rama Hari, based on the Ramayana," Modi tweeted.
"Various parts of the Ramayana were beautifully highlighted in the Rama Hari.
This shows our deep historical bonds and shared heritage."
Modi also said that the Ramayana is widely popular among the southeast Asian nations and complimented the cast and crew of Rama Hari for their "stupendous performance".
Modi arrived here on Sunday on a three-day visit to the Philippines during the course of which he will attend the 15th India-Association of Southeast Asian Nations (Asean) Summit and the 12th East Asia Summit on Tuesday.
Later on Monday, Modi is scheduled to hold bilateral meetings with US President Donald Trump and Filipino President Rodrigo Duterte.
More such meetings with visiting leaders are being arranged on the sidelines of the summits.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)