Some state governments are considering imposing new lockdowns. A hard-hitting nationwide lockdown that started 25 March is gradually being eased because of the damage caused to the economy.
The virus has particularly hit India's densely populated cities and there are now major concerns for New Delhi which has overtaken Mumbai with nearly 80,000 cases.
The city's government has predicted it will have 500,000 infections by the end of July. It is already using railway carriages to house patients and has taken over hotels and banquet halls to relieve the pressure on hard-pressed hospitals.
The government has been criticised over a lack of testing that experts say has hidden the true number of cases in India, which now stands at 509,000.
The country is currently fourth in the world for the number of infections, behind the United States, Brazil and Russia, though it has a much lower death toll.
In a bid to boost tracing efforts, Delhi authorities have called in 33,000 health workers to screen about two million people in sealed off zones across the city of 20 million people.
But cities across the nation of 1.3 billion people are braced for a huge wave of new cases in coming weeks.
"It is likely that we're going into a state, unless we are able to reinforce a strict physical distancing mechanism or a hard lockdown, where the rate of infection will continue to increase," said Anant Bhan, a leading public health expert.
"Unlike China, where the pandemic was relatively more concentrated around Wuhan and a few other cities, India has a more diffused spread that makes it a bit more challenging for the healthcare system," he told AFP.
Mr Bhan said India might see several peaks in coming months because the spread of the virus "is variable across the country".
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