Forex traders said easing crude oil prices also supported the domestic unit.
At the interbank foreign exchange the rupee opened at 71.43, then gathered momentum and touched 71.40 against the US dollar, registering a rise of 10 paise over its previous close.
On Tuesday, rupee had settled for the day at 71.50 against the US dollar.
The domestic unit however could not hold on to the gains and was trading at 71.45 against the dollar at 0935 hrs.
Forex traders said investors were optimistic about the US-China trade talks.
Top Chinese and US trade negotiators have reportedly spoken on phone and agreed to continue to work toward a preliminary agreement for resolving their tariff war.
Domestic bourses opened on a positive note on Wednesday with benchmark indices Sensex trading 213.80 points higher at 41,035.10 and Nifty higher by 64.80 points at 12,102.50.
The dollar index, which gauges the greenback's strength against a basket of six currencies, rose by 0.06 per cent to 98.31.
Market participants, however, said sustained foreign fund inflows supported the local currency.
Foreign institutional investors (FIIs) remained net buyers in the capital market, as they purchased shares worth Rs 4,677.75 crore on Tuesday, according to provisional exchange data.
Brent crude futures, the global oil benchmark, fell 0.23 per cent to trade at USD 64.12 per barrel.
The 10-year government bond yield was at 6.49 per cent in morning trade. DRR DRR