Here are the 10 latest developments in this story:
The PM and President Obama are expected to discuss a wide range of issues including economic and strategic partnerships.
PM Modi approached the West Wing of the presidential complex in a black sports utility vehicle, after driving through a colour guard of US troops and Marines in ceremonial dress.
Typically, visiting heads of state spend just a portion of a day at the White House meeting with President Obama and other US leaders. The second day of attention from President Obama is rare.
In a joint editorial in the Washington Post today, the PM and President Obama said "the true potential of our relationship has yet to be fully realized" and pledged to correct that.
Last night, the PM met President Obama, Vice President Joe Biden and other key US officials at the White House for dinner. 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 strictly every year.
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 - several cabinet level delegations have visited him in Delhi.
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.
"We Revived Nalanda University, Now We Must Revive Nalanda Spirit": PM Modi "Secular Civil Code Need Of Times": PM Modi In Independence Day Speech "Strictest Punishment For Crimes Against Women": PM Amid Kolkata Protests 150 mg Semen In Kolkata Doctor's Body, Suspect Gang-Rape: Parents To Court Tear Gas Fired After Kolkata Protest Against Doctor's Rape-Murder Turns Violent 2 French Rafale Jets Collide Mid-Air, Instructor, Pilot Missing Bangladeshi Students On Alert, To Remain On Streets To Resist Chaos India's 78th Independence Day: A Tribute By Google Doodle "Full Of Negativity...": PM Slams Opposition In Independence Day Speech Track Latest News Live on NDTV.com and get news updates from India and around the world.