Protesters carried their own torch, running from the embankment of the Yamuna River to the Jantar Mantar observatory, where they were met by some 1,500 other protesters and held a rally.
The Indian leg of the relay will be held under unprecedented security, with a short route of only 2.5 km (2 miles) starting at Rajpath Avenue and ending at the India Gate.
Pro-Tibet activists and groups critical of China's rights record have already disrupted the Olympic torch relay in London, Paris and San Francisco, turning the event into an embarrassment for China, which will host the Olympic Games on August 8-24.
About 100,000 Tibetans and their exiled spiritual leader, the Dalai Lama, live in India. Tibetans earlier warned that they would stage mass protests against the Olympic torch's route in India.
The unrest in Tibet started on March 10 when Buddhist monks held a demonstration to mark the 49th anniversary of a failed uprising against Chinese rule, which erupted into widespread protests on March 14.
Several European leaders have said they may boycott the Olympic opening ceremony over China's crackdown on the protests and refusal to negotiate with the Dalai Lama.
Exiled Tibetans say Chinese forces killed around 140 demonstrators, while Beijing says only 18 people were killed, almost all of them Han Chinese murdered by Tibetan separatists.