Here are the latest developments in this story:
After a working lunch with members of both delegations, PM Modi and President Obama walked together in the lawns of Hyderabad House in Delhi deep in talks. They then sat down to a cup of tea that PM Modi poured.
Sources said the US has withdrawn a demand to track the nuclear material it supplies to India. New Delhi had said the demand was intrusive.
A joint statement by the two leaders is expected shortly after delegation level bilateral discussions that are on now.
President Obama and his wife Michelle landed in Delhi a little before 10 this morning. In a departure from protocol, PM Modi received them at the airport. He greeted President Obama with a hug and the leaders shook hands.
President Obama was given a 21-gun salute in a ceremonial welcome at the Rashtrapati Bhawan, where he greeted President Pranab Mukhejee and Prime Minister Narendra Modi with a namaste.
"I am grateful for the extraordinary hospitality, it's a great honour to be back in India," the US president said after inspecting a Guard of Honour led by a woman officer of the Indian Air Force, Wing Commander Puja Thakur.
President Obama has been invited by PM Modi to be the chief guest at the Republic Day celebrations tomorrow. He will be the first US president to be chief guest at the Republic Day parade. He is also the first US president to visit India twice.
This afternoon, he also visited Rajghat where he paid tribute to Mahatma Gandhi and planted a sapling. Asked about his reception in India so far, Mr Obama said, "It's hard to match this one."
The US President will attend a state banquet hosted by President Mukherjee at the Rashtrapati Bhavan this evening. Sources said 250 guests have been invited for the banquet.
A little after he arrived in India the White House tweeted, "President Obama is honored to be back in #India to celebrate Republic Day and to begin a new chapter in the US-India partnership. Jai Hind!" The president's car, called the beast, has both the US and the Indian flags on it today.
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