The rupee opened strong at 71.24 at the interbank forex market then gained further ground to touch 71.19 per dollar, displaying gains of 19 paise against the greenback.
Forex traders said concerns over fiscal slippage and rising coronavirus outbreak fears still remain.
The next trigger for the currency will be the Reserve Bank of India's monetary policy meeting, as its commentary on inflation and well as growth forecast would be keenly watched, they said.
The Reserve Bank of India is scheduled to hold its Monetary Policy Committee (MPC) during February 4-6, 2020.
Meanwhile, rising crude prices, foreign fund outflows and strengthening of the American currency weighed on the local unit.
On Monday, the rupee had settled at 71.38 against the US dollar.
Foreign institutional investors sold equities worth Rs 1,200 crore on a net basis on Monday, according to provisional exchange data.
The benchmark BSE Sensex was trading with gains of 476.82 points, or 1.23 per cent to quote at 40,349.13 while the NSE Nifty was trading at 11,851.55, up 143.65 points, or 1.23 per cent.
Meanwhile, brent crude, the global benchmark, was trading at USD 54.57 per barrel higher by 0.40 per cent.
The 10-year government bond yield was at 6.50 per cent in morning trade. DRR DRR