Forex traders said market participants were enthused following positive developments on the US-China trade talk front and last week's general election win for Britain's Prime Minister Boris Johnson.
At the interbank foreign exchange the rupee opened at 70.96, registering a rise of 4 paise over its previous close.
On Monday, rupee had settled for the day at 71.00 against the US dollar.
The domestic unit, however, could not hold on to the gains and was trading at 70.98 against the dollar at 0947 hrs.
Besides, higher opening in domestic equities and foreign fund flows supported the local unit.
Domestic bourses opened on a positive note on Tuesday with benchmark indices Sensex trading 245.65 points higher at 41,184.37 and Nifty up 64.35 points at 12,118.30.
Foreign institutional investors (FIIs) remained net sellers in the capital market, as they purchased shares worth Rs 728.13 crore on Monday, according to provisional exchange data.
Market participants, however said that rising crude prices weighed on the local currency.
Brent crude futures, the global oil benchmark, rose 0.02 per cent to trade at USD 65.35 per barrel.
However, strengthening of the American currency vis-a-vis other currencies overseas weighed on the rupee. The dollar index, which gauges the greenback's strength against a basket of six currencies, rose by 0.06 per cent to 97.08.
The 10-year government bond yield was at 6.78 per cent in morning trade. DRR DRR DRR