"Deepening partnership with common developmental objective and address global challenges," External Affairs Ministry spokesperson Raveesh Kumar tweeted.
The participating leaders posed for a group photograph ahead of the summit.
Leaders of the 10 Association of Southeast Asian Nations (Asean) states - Brunei, Cambodia, Indonesia, Laos, Malaysia, Myanmar, the Philippines, Singapore, Thailand and Vietnam - and of Australia, China, India, Japan, New Zealand, Russia, South Korea and the US hold this annual summit.
The forum provides an opportunity for the leaders to exchange views and assess international issues of concern, including traditional and non-traditional security threats, primarily terrorism, maritime cooperation and security and non-proliferation.
Modi arrived here on Sunday on a three-day visit to the Philippines, the first prime ministerial visit to this country in 36 years since the visit of Indira Gandhi in 1981.