Traders were also awaiting fresh cues on the potential US-China trade deal
The Indian rupee opened on a cautious note and fell 16 paise to 72 per US dollar in early trade on Tuesday amid rising demand for the US dollar vis-a-vis other currencies overseas and unabated foreign fund outflows.
Forex traders said trading in emerging market currencies were subdued tracking cautious opening in domestic equities.
At the interbank foreign exchange, the rupee opened at 71.97 then fell to 72 against the US dollar, showing a decline of 16 paise over its previous close.
The Indian rupee on Monday had closed at 71.84 against the US dollar.
Traders were also awaiting fresh cues on the potential US-China trade deal.
Meanwhile, brent crude futures, the global oil benchmark, fell 0.24 per cent to USD 62.29 per barrel.
Foreign institutional investors (FIIs) remained net sellers in the capital markets, pulling out Rs 270.66 crore on Monday, as per provisional data.
Domestic bourses opened on a cautious note on Tuesday with benchmark indices Sensex trading 20.27 points higher at 40,304.46 and Nifty up by 4.80 points at 11,889.30.
The dollar index, which gauges the greenback's strength against a basket of six currencies, rose by 0.01 per cent to 97.80.
The 10-year government bond yield was at 6.48 per cent in morning trade.