The US president said he desired to share his vision of how the two countries could strengthen their bilateral relationship.
"Today, I want to speak directly to you, the people of India, about what I believe we can achieve together and how we can do it.
"My commitment to a new a chapter flows from the deep friendship between our people. Michelle (the First lady) and I felt it ourselves," he said in the last public engagement of his three-day state visit to India.
During the visit, Obama was the chief guest at the 66th of the Republic Day parade here Monday.
"With the tricolor above us we celebrated the strength of your constitution... in yesterday's parade we saw the pride and diversity of this nation," he said, adding that it was a great honour for him to be the first American president to attend the Republic Day parade.