The NSE Nifty 50 index was down 0.6% at 16,118.40, as of 0345 GMT, while the S&P BSE Sensex fell 0.53% to 54,109.00.
Investors' focus will be on macro data, which includes India's retail inflation reading due later in the day, as well as the consumer price index from the United States on Wednesday.
A spike in inflation would keep central banks on the path of aggressive rate hikes.
Meanwhile, the Reserve Bank of India (RBI) said on Monday it was putting in place a mechanism for international trade settlements in rupees, which banks will need a prior approval to use.
The RBI's move comes as the Indian rupee touches all-time lows amid continued foreign portfolio outflows from domestic stock markets and a broadly stronger greenback.
(Reporting by Nallur Sethuraman in Bengaluru; editing by Uttaresh.V)