PM Modi's comments came ahead of his bilateral talks with President Trump on the sidelines of the ASEAN summit in Manila during which the two leaders discussed a range of key issues including defence and security.
"The relations between India and the US are growing, and I also feel that the relationship between India and the US is not only for mutual interest. It goes beyond that. We are working together for the interest, for the future of Asia and for the humanity as a whole in the world," PM Modi said.
PM Modi also thanked the US president for praising India whenever he got an opportunity to speak about the country during his Asia tour.
"...in the few days wherever president Trump has travelled and whenever opportunity arose to talk about India, he has expressed very high opinion about India," PM Modi said.
"I would like to assure you whatever the expectations are of the world, of the US from India, India has always made efforts to fulfil those expectations and we will continue to do so in the future too," he said.
Donald Trump on his part described PM Modi as a friend and a great gentleman.
"PM Narendra Modi is here we had met at the White House before. He has become a friend of ours. He's doing a great job. A lot of things were solved and we will continue to work together," he said.
The two leaders are understood to have discussed the security scenario in the region besides several other issues of mutual interests, including ways to further boost bilateral trade.
The move to set up the quadrilateral alliance of India, US, Japan and Australia comes in the backdrop of growing Chinese assertiveness in the South China Sea. The US has been favouring a larger role for India in the strategically important Indo-Pacific region.
The use of the term "Indo-Pacific" by President Trump has led to speculation that it may have something to do with Washington preparing the ground for a revival of the so called quadrilateral strategic alliance between the US, Japan, Australia and India to counter China's rise.
President Trump on Saturday praised India's "astounding" growth after it opened up its economy and also lauded PM Modi, saying he has been working successfully to bring the vast country and its people together.
Speaking at a gathering of CEOs on the sidelines of the annual Asia-Pacific Economic Cooperation (APEC) summit in the Vietnamese city of Danang, President Trump had cited India as one of the countries in the Indo-Pacific region making strides.
He praised India as a sovereign democracy with a population of over 1 billion as well as the largest democracy in the world.