A woman receives a shot of Covishield vaccine at a club in Siliguri, India, on Monday. AFP

India gave out a record 7.5 million vaccine doses on Monday under a federal campaign to inoculate all adults for free.

"If supply remains consistent, we will be on course to innoculate most of our population by the end of the year, DN Patil, a senior health official in the country's richest state of Maharashtra said.

Maharashtra has a population of more than 125 million.Earlier this month, the government said India could have as many as 10 million doses of COVID-19 vaccines available per day in July and August.

Healthcare workers cross Mundeswari river to inoculate villagers with Covishield vaccine. Reuters

Government adviser Vinod Kumar Paul said on Monday that administering 10 million shots per day was not a "set goal."

"As the ramping up takes place, speed of implementation should also ramp up and that would lead to a certain number," Paul said in an interview with CNBC-TV18 channel.

Meanwhile, Prime Minister Narendra Modi kicked off a muted International Yoga Day hailing the practice's "protective" properties against the coronavirus.

Bollywood actress Shilpa Shetty gestures while performing yoga at her home in Mumbai on Monday to mark International Yoga Day. AFP

So far India has administered 280 million shots, with barely four per cent of people fully vaccinated. The government aims to inoculate all of India's almost 1.1 billion adults by the end of the year.

Public parks were re-opened in Delhi on Monday, but the number of events for Yoga Day was cut back around the country for the second year running because of the pandemic.

"The vaccination drive is expected to pick up speed now... the daily vaccination has picked up over the last week and is expected to strengthen further," community health expert Rajib Dasgupta said.

"However, both existing inequities as well as hesitancy merit deeper attention to make this a success."

Healthcare workers carry Covishield vaccine to inoculate villagers in  West Bengal state. Reuters 

The free roll-out came as Modi marked the annual Yoga Day event with an early-morning address to the nation as it emerges from the surge, saying the practice had again proved itself to be a source of "inner strength."

"When I speak to frontline warriors, they tell me that they have adopted yoga as a protective shield in their fight against coronavirus. Doctors have strengthened themselves with yoga and also used yoga to treat their patients," Modi said.

Yoga Day - proposed by Modi and adopted by the United Nations in 2014 - is observed mostly in India, but also worldwide on the Northern Hemisphere's longest day.

Naval personnel perform yoga onboard of the INS Trikand in the Gulf of Aden, to mark International Yoga Day. AFP

The country's vaccination drive has significantly slowed in recent months due to a shortage of jabs and hesitancy, even as it battled a vicious surge in cases in April and May that overwhelmed the healthcare system in many places.

Case numbers have since fallen sharply and the authorities have again relaxed many restrictions, sparking fears of another wave.

The government had expanded the vaccine roll-out to include all adults aged below 45 on May 1, but states and private hospitals had to procure and buy the shots themselves for the younger age group, leading to confusion and shortages.

Agencies