Mr Obama watched the parade with Mr Modi inside a bullet-proof glass enclosure
US President Barack Obama has attended India's Republic Day parade in Delhi, the first US head of state to do so.
Mr Obama was chief guest at the annual military parade. He arrived on Sunday for a three-day visit seen as a sign of warming ties between the two countries.
After talks on Sunday, both sides announced a breakthrough on a pact that will allow US companies to supply India with civilian nuclear technology.
Indian PM Narendra Modi said it was a "new journey" of co-operation.
Mr Obama will meet the main opposition Congress party leaders later on Monday and will also speak at a business summit.
Trade vow
Republic Day marks the adoption of India's constitution in 1950, three years after independence from Britain.
Uniformed soldiers in colourful headgear marched down Rajpath, or King's Avenue, where Mr Obama watched the parade with Mr Modi inside a bullet-proof glass enclosure.
The BBC's Sanjoy Majumder in Delhi says the ceremony showcased India's military might with soldiers marching in formation and the latest weapons on display, including several that are American-made.
Huge crowds and thousands of security personnel attended the Republic Day parade
Helicopters showered petals on the crowds and brass bands and dancers filed past the guests on a foggy and rain-hit morning.
"The day is all about patriotism and I'm lucky to be a part of it," Ajith Kumar, a student watching the parade, said. "The fact that we have a guest like Obama has made it all the more special."
The US president received a warm welcome on Sunday when Mr Modi greeted him at the airport with a bear hug.
The two men spent several hours discussing defence 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.
Rain failed to dampen spirits with thousands turning up to watch the Republic Day parade
Mr Modi's colourful headgear attracted a lot of attention
Indian dancers also performed at the parade
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 $100bn (£66.7bn) a year, and build co-operation on defence projects.
Mr Obama's visit to India has been shortened so he can visit Saudi Arabia and pay his respects following the death of King Abdullah. It means he and his wife, Michelle, will not now visit the Taj Mahal.