After summit talks with President Obama for over 90 minutes at his Oval Office in the White House, Mr Modi said the conversation had strengthened his belief that India and the US are "natural partners."
The two leaders covered a broad range of issues including economic cooperation, trade and investment and Mr Modi said he had sought Mr Obama's support for ease of access for Indian services companies in the US market.
Speaking in Hindi, the PM said he hoped for rapid growth in India's economic partnership with the US, adding, "We are focusing not just on policies but on processes to make it easier to do business in India."
He invited American companies to participate in the Indian defence manufacturing sector, even as the two countries decided to extend their defence cooperation agreement for ten more years.
Seated beside Mr Modi, Mr Obama said, "Throughout this conversation, I'm impressed with the Prime Minister's interest in not only addressing the needs of the poorest of the poor in India and revitalising the economy there, but also his determination to make sure that India is serving as a major power that can help bring about peace and security to the world."
Mr Modi also said he had "a candid discussion" with President Obama about India's move to block a key World Trade Organisation pact that would streamline customs procedures and boost global commerce. "India supports trade facilitation. However, I also expect that we are able to find a solution that takes care of our concern on food security. I believe that it should be possible to do that," Mr Modi said.
The Prime Minister has invited Mr Obama and his family to visit India.
Mr Modi, who was denied a visa to the United States in 2005 on human rights grounds over communal riots in his home state of Gujarat three years before that, has been courted heavily by the US since he took office.
On this trip, he has received a warm welcome, speaking at the UN General Assembly, addressing a full-house audience at New York's Madison Square Garden and meeting with 17 top US CEOs.