The country has so far vaccinated 631,417 frontline workers using two shots manufactured locally, one licensed from Oxford University and AstraZeneca and another developed at home by Bharat Biotech in partnership with the state-run Indian Council of Medical Research.
The drive started on Saturday, with 30 million healthcare and other front-line workers first in the queue, followed by about 270 million people older than 50 or deemed at high-risk because of pre-existing medical conditions.
The health ministry said India inoculated more people on its first day than the United States, Britain or France. But it said it expected a greater number of volunteers, especially in major states such as Tamil Nadu and Punjab, lagging other states.
Vinod K Paul, who heads a government committee on vaccine strategy, told a news conference health workers who failed to take vaccine doses set aside for them were not fulfilling their "societal responsibility".
"Please understand the whole world is clamouring for vaccines," said Paul. "If our healthcare workers, our doctors and nurses, if they are declining to take it, I feel sorry," he said. "I plead with them, on behalf of the government, because we don't know what shape this pandemic will take going forward."
India, the world's biggest manufacturer of vaccines, announced it will begin exporting shots on Wednesday.
On Tuesday it reported 10,064 infections, the fewest in seven months, taking the total to 10.58 million. Deaths rose by an eight-month low figure of 137, taking the overall tally to 152,556.
Some doctors have expressed doubt about the Bharat Biotech vaccine, which was given approval for emergency use without efficacy data from late-stage clinical trials. The government says it is safe and effective. Paul said he received his own shot of the it on the first day.
Paul has told Reuters both vaccines will be treated equally. Recipients will not be allowed to choose between them for now.
In a survey conducted by New Delhi-based online platform LocalCircles, 62% of 17,000 respondents were hesitant to get vaccinated immediately, mainly due to worries over possible side-effects. The government has reported hospitalisation from side effects in only 0.002% of vaccine recipients.
State officials have told Reuters vaccinations were slowed by glitches in a government online platform.
"It's slow, that is why we have taken a decision at our level - we are informing people by our own system of SMS so that we are able to achieve 100%," Pradipta Mohapatra, the top health bureaucrat in the eastern state of Odisha, told Reuters.
"At the end of the day people need to be vaccinated."