India has recorded its biggest single-day spike in coronavirus cases as the government eased one of the world's strictest lockdowns to allow some manufacturing and agricultural activity to resume.

An additional 1,553 cases were reported over 24 hours, raising the national total past 17,000 on Monday. At least 543 people have died from COVID-19, the respiratory disease caused by the virus, and epidemiologists forecast the peak may not be reached before June.

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The nationwide lockdown imposed on March 24 halted all but essential services, sparking an exodus of migrant workers and people who survive on daily wages out of India's cities and towards villages in rural areas.

Authorities picked up travellers in a fleet of buses and quarantined many of them in empty schools and other public buildings for 14 days.

Starting on Monday, limited industry and farming were allowed to resume where employers could meet social distancing and hygiene norms and migrant workers were allowed to travel within states to factories, farms and other work sites.

"In the event a group of migrants wish to return to their places of work within the state where they are presently located, they would be screened and those who are asymptomatic would be transported to their respective places of work," India’s home ministry said in a letter to state governments.

However, government surveys in the central Indian state of Maharashtra, the worst-hit by the virus, have suggested the few companies eligible to restart operations can do so because they are required to transport and shelter workers as a virus-prevention measure.

While a partial lifting of a curfew permitted the restart of coal plants and oil refineries, animal feed and agro-industry and other labour-intensive manufacturing such as brick kilns, much of the country remained under lockdown.

India's airspace was closed to commercial traffic, its passenger rail system, buses and metros were halted, e-commerce was restricted to food and other essentials, and schools, stadiums and houses of worship remained closed until May 3.

India is also continuing to ramp up testing, build up stocks of ventilators and personal protective equipment and prepare makeshift isolation wards and dedicated COVID-19 hospitals.

In Mumbai, the capital of Maharashtra and home to one of Asia's largest slums, city authorities were planning to administer hydroxychloroquine to thousands of slum-dwellers over 14 days to gauge whether the drug helped to slow the spread of the disease in a place where social distancing norms are not possible to achieve.

It was unclear how many people would participate in the experiment, or when it would begin.

President Donald Trump has touted the malaria drug to treat COVID-19, though its efficacy against the disease is unproven.