Narendra Modi did stretches, bends and breathing exercises with 35,000 school children, bureaucrats and soldiers.
Security was tight in the Indian capital with thousands of police and paramilitary deployed for Sunday morning’s event.
Millions of others are expected to do yoga at similar events planned in hundreds of Indian cities and towns.
Narendra Modi, a yoga enthusiast who says he practices the ancient Indian art daily, lobbied the United Nations to declare June 21 International Yoga Day.
Thousands of colorful mats were laid out on Rajpath – King’s Avenue – where the main event was held.
Officials had earlier said PM Narendra Modi will attend the event and address the gathering, but not do yoga.
However, the prime minister surprised participants by joining in with the exercises.
Authorities said 35,000 people attended the 35-minute yoga session on Rajpath, aimed at setting a new Guinness World Record for the largest yoga class at a single venue.
Guinness officials said they would announce the results in a few hours.
Yoga was also being performed on the Siachen glacier and the high seas, the defense ministry said.
The day is also being celebrated around the world and Indian Foreign Minister Sushma Swaraj says “tens of millions” will do yoga on Sunday, June 21.
Sushma Swaraj herself will be in New York where she will attend the celebrations with UN Secretary General Ban Ki-moon. In Times Square, 30,000 people are expected to do yoga.
However, the day, being billed as one to promote “harmony and peace”, has hit a controversial note with some Muslim organizations saying yoga is essentially a Hindu religious practice and is against Islam.
Many others say Narendra Modi’s Hindu nationalist government has an agenda in promoting the ancient Indian discipline.
However, the authorities deny the charge – they say participation in the yoga day is not mandatory and reports that Muslims are opposed to yoga are exaggerated.
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