India's nationwide coronavirus lockdown, the biggest in the world covering 1.3 billion people, will be extended until May 3, Prime Minister Narendra Modi said Tuesday.

The move comes despite complaints from millions of poor, a vast underclass who have been left almost completely without support as jobs have vanished and incomes dried up.

"From the economic angle, we have paid a big price," Modi said. "But the lives of the people of India are far more valuable."

"From the experiences of the last few days it is clear that the path we have chosen is correct."

India's three-week-old lockdown, in force since March 25, was scheduled to end at midnight Tuesday.

Modi said there would be "limited relaxations" from April 20 for districts with no cases, and new guidelines for industry and agriculture would be released Wednesday.

The announcement comes as debate rages around the world on how to lift restrictions so the economic carnage of the pandemic can be eased without a new spike in infections.

Official figures suggest South Asian nations have so far been relatively unscathed by the epidemic, with around 10,800 cases and 353 deaths in India.

Some experts say not enough tests have been conducted and the true number of infections is much higher.

Several states including Maharashtra - home to Mumbai and with the highest number of cases - Tamil Nadu and Odisha already announced lockdown extensions.

The World Health Organisation Tuesday praised India's decision to extend the lockdown, saying "it would go a long way in arresting the virus spread".

The shutdown, with strict limits on activity, has been devastating for the economy - and in particular for India's poor.

Millions of daily wage labourers suddenly lost their jobs, forcing hundreds of thousands to travel hundreds of kilometres (miles) back to their home villages, often on foot. Some died on the way, while others were shunned by locals when they made it back.