Barack Obama is the first US president to attend India’s parade, on the second day of his visit.
The president arrived in India on January 25 for a three-day visit seen as a sign of warming ties between the two countries.
On Sunday, both sides announced a breakthrough on a pact that will allow US companies to supply India with civilian nuclear technology.
Indian Prime Minister Narendra Modi said it was a “new journey” of co-operation
Barack Obama will meet the main opposition Congress party leaders later on Monday and will also speak at a business summit.
India’s Republic Day marks the adoption of the country’s constitution in 1950, three years after independence from Britain.
Uniformed soldiers in colorful headgear marched down Rajpath, or King’s Avenue, where Barack Obama watched the parade with Narendra Modi inside a bullet-proof glass enclosure.
Helicopters showered petals on the crowds and brass bands and dancers filed past the guests on a foggy and rain-hit morning.
Barack Obama received a warm welcome on Sunday when Narendra Modi greeted him at the airport with a bear hug.
The two men spent several hours discussing defense and trade ties, and then announced the breakthrough on the civilian nuclear deal.
The pact was agreed in 2008 but has been held up for six years because of differences over the liability US firms would face in India in the event of a nuclear accident.
Now a large insurance pool will be set up, without the need for any further legislation.
The two sides have also pledged to increase their bilateral trade five-fold, from the current $100 billion a year, and build co-operation on defense projects.
Barack Obama’s visit to India has been shortened so he can visit Saudi Arabia and pay his respects following the death of King Abdullah.
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