Kovind received the ASEAN heads of state and government at the Rashtrapati Bhavan and hosted a lunch in their honour.
The president, on the occasion, said that India's 'Act East policy' reinforces its ancient links with Southeast Asia through enhanced political, security, economic and cultural ties.
"In this context, India greatly values ASEAN's role as a proponent of peace, stability and prosperity in the region,"
Kovind said and reiterated India's support to ASEAN's unity and centrality.
"We stand shoulder-to-shoulder with ASEAN in pursuit of a rules-based regional architecture that is open, inclusive, balanced and equitable," he said.
The president said that India and ASEAN are bound by history and geography.
"Culture, commerce and connectivity -- and ideas and thought -- have woven us together in one common fabric. Our partnership is based on our shared heritage and is built on the foundation of strong people-to-people contacts, nurtured through the millennia," he said.
Kovind said that India-ASEAN relations have come a long way since India established a dialogue partnership with ASEAN on January 28, 1992.
ASEAN is a strategic partner for India, he said.
"We have 30 dialogue mechanisms between India and ASEAN, including annual summits and seven ministerial meetings in a wide range of sectors," Kovind said.
The Association of Southeast Asian Nations (ASEAN) comprises Thailand, Vietnam, Indonesia, Malaysia, the Philippines, Singapore, Myanmar (Burma), Cambodia, Laos and Brunei.
The 10 ASEAN heads of state and government who visited the Rashtrapati Bhavan included Brunei's Sultan Haji Hassanal Bolkiah, Indonesian President Joko Widodo, Philippines President Rodrigo Roa Duterte, Cambodian Prime Minister Hun Sen and Singaporean Prime Minister Lee Hsien Loong.
Malaysian Prime Minister Najib Razak, Thailand's Prime Minister General Prayut Chan-o-cha, Myanmar's State Counsellor Aung San Suu Kyi, Vietnamese Prime Minister Nguyen Xuan Phuc and Lao PDR's Prime Minister Thongloun Sisoulith also attended the lunch.
These leaders are in India to attend the ASEAN-India Commemorative Summit.
They will also be guests of honour at India's 69th Republic Day celebrations on January 26.