Here are 10 big developments on their meeting:
The PM met President Obama, Vice President Joe Biden and other key US officials at the White House for dinner on Monday, ahead of formal talks at the Oval Office on Tuesday.
The PM and President Obama sat down under a gilded chandelier in the antique-festooned Blue Room of the White House.
The PM sipped only water at the dinner; he is keeping the nine-day Navratri fast that he observes every year.
In a joint statement issued after their first meeting at a White House dinner, the two leaders said they would work together on "a transformative relationship as trusted partners".
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 enjoyed a warm welcome in the US.
Since he took office, Washington has made strenuous efforts to court him - sending several cabinet level delegations to New Delhi and pushing for an early visit to the United States.
The United States has been keen to expand business and security ties with India, which it sees as a key counterbalance to an increasingly assertive China in Asia.
President Obama has backed Delhi's bid to become a permanent member of the UN Security Council.
As part of an effort to spur foreign investment, the PM met more than a dozen US corporate leaders for breakfast in New York on Monday and told them he is committed to liberalizing India's economy and slashing the country's infamous red tape.
He said that despite some differences with Washington, the wider relationship could still improve. "It is not necessary we should have comfort in everything, even between a husband and wife, there is never 100 percent comfort," Mr Modi joked at the Council on Foreign Relations on Monday.
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