A sanitation worker became the first Indian to receive a Covid vaccine as the country began the world's largest inoculation drive.
Prime Minister Narendra Modi launched the programme, which aims to vaccinate more than 1.3 billion people against Covid.
He paid tribute to front-line workers who will be the first to receive jabs.
India has recorded the second-highest number of Covid-19 infections in the world after the United States.
Millions of doses of two approved vaccines - Covishield and Covaxin - were shipped across the country in the days leading up to the start of the drive.
"We are launching the world's biggest vaccination drive and it shows the world our capability," Modi, said, addressing the country on Saturday morning.
He added that India was well prepared to vaccinate its population with the help of an app, which would help the government track the drive and ensure that nobody was left out.
Modi spoke at length about doctors, nurses and other front-line workers "who showed us the light" in "dark times".
"They stayed away from their families to serve humanity. And hundreds of them never went home. They gave their life to save others. And that is why the first jabs are being given to healthcare workers - this is our way of paying respect to them."
Modi also appealed to people to continue adhering to Covid-19 safety protocols like wearing masks and following social distancing. He said the country cannot afford to be complacent as vaccinating the entire population will take time.
He also urged people not to believe any "propaganda and rumours about the safety of the vaccines".
"I want to tell people that the approval to these vaccines was given only after scientists and experts were satisfied about its safety," he said.
An estimated 10 million health workers will be vaccinated in the first round, followed by policemen, soldiers, municipal and other front-line workers.
Next in line will be people aged over 50 and anyone under 50 with serious underlying health conditions. India's electoral rolls, which contain details of some 900 million voters, will be used to identify eligible recipients.
The government plans to vaccinate 300 million people by early August. This will happen in state-run health care centres, schools, colleges, community halls, municipal offices and wedding halls.
Several hospitals across India are giving the first doses of the vaccine.
Dr Atul Peters was among those who got the jab at Max hospital.
"It's a very big day. I'm grateful to those who worked hard to make this a reality. I was very very happy when I got a call informing me that my name was on the list.
"We worked hard during the pandemic to save lives and we are also taking the jab first to dispel fears in people's minds that the vaccine is not safe," he told the BBC.
India's drug regulator has given the green light to two vaccines - Covishield (the local name for the Oxford-AstraZeneca vaccine developed in the UK) and Covaxin, locally-made by pharma company Bharat Biotech.
But concerns have been raised over the efficacy of Covaxin because the regulator's emergency approval came before the completion of Phase 3 clinical trials. The regulator and the manufacturer have said the vaccine is safe, and that the efficacy data would be available by February.
Both vaccines will be given as two injections, 28 days apart, with the second dose being a booster. Immunity would begin to kick in after the first dose but reaches its full effect 14 days after the second dose.
The status of the vaccines and recipients will be electronically tracked in real time - some 8 million people who will receive the early jabs have been already registered. More than 600,000 people have been trained for the drive.
The jabs will be voluntary, and recipients will be given a certificate of vaccination after they complete both doses.
"I expect India's vaccination programme will be run much better than most countries because of the considerable government investment and early preparedness," Dr Gagandeep Kang, one of India's best-known vaccine experts, told the BBC.
- BBC