Given India's population density, experts have long worried that a sustained COVID-19 outbreak would lead to pressure on its stretched healthcare system.

Prime Minister Narendra Modi lifted most restrictions which had been part of an almost three-month nationwide lockdown on June 8, despite the continuing rise in cases.

Data from India's federal health ministry on Friday showed an additional 13,500 infections over the previous 24 hours, with more than 300 deaths.

India is behind only the United States, Brazil and Russia in total infection numbers and has reported four times more than China, which has a similar population.

On Friday, the southern state of Tamil Nadu imposed a lockdown with tough restrictions in Chennai and surrounding districts until June 30.

Roads in Chennai, known as "India's Detroit" for its large car-making industry, were largely empty on Friday and most shops were closed amid heavy police patrolling to ensure adherence to the rules.

"Police officers and medical professionals are fighting for you. Please cooperate and be hopeful," Tamil Nadu state Health Minister C Vijayabaskar said in a tweet.

"Let's follow social distancing, stay aware and win this battle against this pandemic."

Tamil Nadu has tested more than 800,000 people for COVID-19 - the highest number in the country - and its mortality rate is almost a third of the national average. But it has been facing criticism over delayed reporting of deaths, and the number of cases and casualties has been rising steeply in recent days, mainly in and around Chennai.

Restrictions elsewhere in India, where states have their own powers to set health rules, have largely been eased.

Roads and businesses in the capital New Delhi, where several politicians including the state health minister have tested positive for the virus, were largely open on Friday.

Australian Associated Press