The NSE Nifty 50 index ended 1.52% higher at 11,300.55, and the S&P BSE Sensex closed up 1.47% at 38,492.95. Both indexes touched their highest levels since early March in the session.

Markets in Europe and Asia booked gains as investors wagered the U.S. Federal Reserve would reaffirm its dovish stance this week, and a tolerance for higher inflation.

Europe's STOXX 600 eked out a 0.2% rise after MSCI's broadest index of Asia-Pacific shares outside Japan <.MIAPJ0000PUS> ended up 0.8%.

U.S. Senate Republicans on Monday also proposed a $1 trillion coronavirus aid package as the virus pandemic has killed nearly 150,000 people in the country.

In Mumbai, the Nifty auto index <.NIFTYAUTO> rose 3.5%, its highest since Feb. 25. Car makers Mahindra and Mahindra and Tata Motors gained about 4.7% each.

India's second-most valuable stock Tata Consultancy Services rose as much as 5.1% and pushed up the Nifty IT index nearly 2.5%.

Ultratech Cement rose 7.2% and topped the Nifty gainers after the company reported a better-than-expected profit for the quarter ended June.

ICICI Bank was the top laggard, shedding 1.8%, followed by Bharti Infratel, which dropped 1.7%.

India's coronavirus cases touched 1.48 million by Tuesday morning, government data showed.

(Reporting by Derek Francis in Bengaluru; Editing by Shinjini Ganguli)