People above 60, and those who are 45 or more and suffering from certain medical conditions, are now eligible for the vaccinations.
India, which has reported the highest number of COVID-19 cases in the world after the United States, has so far vaccinated more than 12 million health and front-line workers.
"Remarkable how our doctors and scientists have worked in quick time to strengthen the global fight against COVID-19," Modi said on Twitter.
Bharat Biotech has said efficacy data from a late-stage trial on nearly 26,000 volunteers who took COVAXIN will be out soon.
The company, along with India's drug regulator, says COVAXIN is safe and effective, based on early and intermediate studies.