India woke up on Wednesday to a sweeping lockdown of its 1.3 billion people, one of the world's most ambitious efforts to fight the coronavirus, but the order didn't stop crowds of people thronging to stock up at grocery shops and chemists.

India's tally of 536 cases and nine deaths seems tiny compared with those in China, Italy and Spain, but Prime Minister Narendra Modi and health experts have warned that the world's second most populous country faces a tidal wave of infections if tough steps are not taken.

Modi ordered the three-week shutdown in a speech to the nation on Tuesday evening, some four hours before it came into effect.

As India's various states shut their borders, long queues of trucks carrying milk, fruits and vegetables snaked down highways.

Modi said essential services would be maintained and people are allowed out to buy groceries and medicines, but transport was off the streets in most places on Wednesday.

"My daughter needs allergy medicines regularly. The medicine shops are open but how do we reach there?" said Yash Goswami in the northern town of Moradabad.

"Who wants to risk a run-in with the police? They're beating people up."

Some shopkeepers in New Delhi also complained of heavy-handed policing because they had opened.

"There are no clear instructions, police are telling us to close," said Ram Agarwal, a grocer in Delhi swamped by people looking to buy dry food and milk.

Other countries in South Asia - home to a quarter of the world's population - are also struggling as they try to put up defences against the coronavirus.

Pakistan's tally of cases rose to 1,000, with seven deaths, its health ministry said.

Authorities have shut down Sindh province, home to its largest city of Karachi, even though Prime Minister Imran Khan said he was opposed to a full lockdown because the poor would suffer the most.

Sri Lanka has sealed itself off from the outside world, suspending all flights in and out of the island nation.

'NO WORK, NO PAY'

In New Delhi, Modi met his cabinet at his residence, with ministers sitting apart from each other in a large room.

"Social distancing is the need of the hour," Home Minister Amit Shah said on Twitter with a picture of the meeting.

Modi's shut-down order echoes other big decisions he has been able to make partly because of his solid support from large parts of the public.

In 2016, he banned most large denomination bank notes to fight graft, throwing a cash-reliant economy into turmoil.

Last year, he stripped the troubled Muslim-majority state of Jammu and Kashmir of its special constitutional status, backing the decision with the detention of scores of politicians and months of communications blackout.

The coronavirus lockdown comes after evidence indicated it was spreading out into India's countless small towns after a first wave in Delhi, the commercial hub of Mumbai and other big cities.

That has raised the prospect of a cash-strapped public health sector being overwhelmed. India has just 0.5 hospital beds for every 1,000 people, compared to 4.3 in China and 3.2 in Italy.

But the consequences of shutting down the $2.9-trillion economy will be far-reaching.

"Asking people to stay at home is necessary but the majority of the population can't afford to sit at home without work and pay," said Madhura Swaminathan, head of the economic analysis unit of the Indian Statistical Institute in the technology hub of Bengaluru.

India, the world's main supplier of generic drugs, on Wednesday banned the export of a malaria drug that is being tested as a coronavirus treatment, saying it had meet domestic demand.

But the lockdown could hit production of hydroxychloroquine because of shortages of staff to run operations, Dinesh Dua, chairman of the Pharmaceuticals Export Promotion Council of India, told Reuters.