India posted a record daily rise of 401,993 new coronavirus cases on Saturday as the country opened up its massive vaccination drive to all adults, although several states warned of acute shortages.

It was the first time India's daily case count had topped 400,000 after 10 consecutive days over 300,000. Deaths from Covid-19 jumped by 3,523 over the past 24 hours, taking the total toll in India to 211,853, according to official data.

The world's biggest producer of Covid-19 vaccines has a limited number of shots available, worsening a grim second wave of infections that has overwhelmed hospitals and morgues while families scramble for scarce medicines and oxygen.

Hundreds of people were seen queuing to be vaccinated across Ahmedabad, the main commercial city in Prime Minister Narendra Modi's home state of Gujarat, on Saturday.

The chief minister of the hard-hit state of Delhi on Friday implored people not to queue at vaccination centres, promising more vaccines would arrive "tomorrow or the day after".

India's eastern Odisha state said on Friday it had received a consignment of 150,000 shots but would only allow a few people to get shots due to lockdown restrictions preventing movement.

A fire in a hospital about 190 kilometres south of Ahmedabad killed 16 coronavirus patients and two staff, the latest in a series of deadly accidents at hospitals.

Modi offered his condolences to the families of the hospital fire victims on Twitter, hours after he posted pictures of himself praying at a Sikh temple in capital New Delhi.

Some experts blame mass religious gatherings and political rallies for the severity of India's second wave, which caught the government unprepared.

A forum of scientific advisers set up by the Modi administration had warned Indian officials in early March of a new and more contagious variant of the coronavirus taking hold in the country, five scientists who are part of the forum told Reuters.

Despite the warning, four of the scientists said the federal government did not seek to impose major restrictions to contain the spread of the virus. Millions, largely unmasked, attended religious gatherings and election rallies that were held by Modi, leaders of the ruling Bharatiya Janata Party and opposition politicians.

The total number of Covid cases in India has topped 19 million. As the second wave has picked up steam, India has added about 7.7m cases since the end of February, according to a Reuters tally. In contrast, it took India nearly six months to add the previous 7.7m cases.

The surge in cases led US President Joe Biden to impose new travel restrictions on India on Friday, barring most non-US citizens from entering the United States.

Australian officials said residents and citizens who have been in India within 14 days of the date they plan to return home will be banned from entering Australia as of Monday, and those who disobey will face fines and jail.

Other countries and territories have also imposed similar travel restrictions on India, including Britain, Germany, Italy and Singapore, while Canada, Hong Kong and New Zealand have suspended all commercial travel with India.