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India's daily rise in coronavirus cases retreated from the 400,000 mark on Monday, while its daily rise in deaths also fell after two straight days of more than 4,000 fatalities.

Calls grew for India to impose a nationwide lockdown as new coronavirus cases and deaths held close to record highs on Monday, increasing pressure on the government of Prime Minister Narendra Modi.

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The health ministry reported 366,161 new COVID-19 infections and 3,754 more deaths. India's total caseload now stands at 22.66 million, with 246,116 deaths.

As many hospitals grapple with an acute shortage of oxygen and beds while morgues and crematoriums overflow, experts have said India's actual figures could be far higher than reported.

Many hospitals in India grapple with an acute shortage of oxygen.

Sunday's 1.47 million tests for COVID-19 were this month's lowest yet, data from the state-run Indian Council of Medical Research showed. The figure compared with a daily average of 1.7 million for the first eight days of May.

The number of positive results from the tests was not immediately clear, however.

Many states have imposed strict lockdowns over the last month while others have placed curbs on movement and shut cinemas, restaurants, pubs and shopping malls.

But pressure is mounting on Modi to announce a nationwide lockdown as he did during the first wave of infections last year.

He is battling criticism for allowing huge gatherings at a religious festival and holding large election rallies during the past two months even as cases surged.

Sunday's 1.47 million tests for COVID-19 were this month's lowest yet.

"A failure of governance of epic and historic proportions," Vipin Narang, a political science professor at the Massachusetts Institute of Technology (MIT) in the United States, said on Twitter.

Sonia Gandhi, the chief of the main opposition Congress party, blamed the government for abdicating its responsibility by leaving vaccinations to states, Reuters partner ANI said on Twitter.

Delhi's health minister said the city was running out of vaccines, with just three to four days of supplies remaining of AstraZeneca's vaccine, made by the Serum Institute of India and branded Covishield, the NDTV news channel reported.

By Sunday, the world's largest vaccine-producing nation had fully vaccinated just over 34.3 million, or only 2.5%, of its population of about 1.35 billion, government data shows.