Some 18,000 individuals took part in an event organised in Rajpath where they performed yoga. The participants included Defence Minister Rajnath Singh.
The New Delhi Municipal Council estimated the number of participants to be even more than 18,000.
It is for the first time that the event did not use plastic yoga mats as they were replaced with Khadi mats.
President Ram Nath Kovind, who took part in an indoor event in Parliament, said in a tweet: "On #InternationalDayofYoga best wishes to all practitioners of yoga across the world. Yoga is India's gift to humanity; it holds the key to healthy living and to that fine balance between mind and body. Do become a part of the celebration of yoga."
In another event organised by the South Delhi Municipal Corporation (SDMC), Union Minister Piyush Goyal and MP Manoj Tiwari along with several other hundred participants performed yoga at the Talkatora Stadium.
Meanwhile, Union Minister Smriti Irani posted pictures of her doing yoga with other participants at an event in Bijwasan.
"Celebrated #YogaDay2019 by performing Yoga with citizens of Bijwasan in Delhi," she captioned the image.
Newly-appointed Lok Sabha Speaker Om Birla participated in an event in Parliament premises.
The Delhi Police also marked the day at the Thyagaraj Sports Complex, where the chief guest was Amulya Patnaik, the Commissioner of Police, Delhi.
( With inputs from IANS )