The Nifty closed down 0.86% at 11,153.65 and the Sensex slipped 0.8% to 37,734.08. Both the indexes fell more than 2% on Monday and have fallen for four straight sessions.

In India, total coronavirus cases touched 5.6 million as of Tuesday. European countries mulled tightening restrictions to curb a sharp resurgence in cases, while the COVID-19 death toll in the U.S. approached 200,000.

"As far as the virus is concerned the second wave is big. That is giving a sense of fear to everyone that there may be some restrictions enforced again, which may hamper the economic recovery," said Neeraj Dhawan, director at Quantum Securities in New Delhi.

The Nifty energy index slid 2%, Nifty realty fell 1.9% and Nifty public sector was down 2.04%, making them the top losers.

Shares of India's largest IT exporter Tata Consultancy services rose as much as 3.64% after the company expanded partnership with UK-based supermarket chain Morrisons.

TCS lifted the IT services subindex on the NSE by 0.7%.

India's federal police said on Monday they had registered a case against dairy company Kwality Ltd and its directors for allegedly cheating a consortium of banks of around 14 billion rupees ($190 million).

Meanwhile, Asian shares were broadly weaker on Tuesday, while European markets clawed back some gains after a sharp sell-off in the previous session.

Shares of steel equipment maker GMM Pfaudler fell 10% after the company said on Monday its promoters planned to sell about 17.6% stake.

By Sethuraman N R