The Indian rupee opened on a flat note and appreciated by 3 paise to 71.32 against the US dollar in early trade on Thursday tracking muted opening in domestic equities.

Forex traders said, the domestic unit was trading in a narrow range as investors await clarity on the US-China trade front.

At the interbank foreign exchange, the rupee opened at 71.33, then gained further ground and touched a high of 71.32, registering a rise of just 3 paise over its previous close.

The domestic unit, however, could not hold on to the gains and was trading at 71.37 against the dollar at 0931 hrs.

On Wednesday, the rupee had settled for the day at 71.35 against the US dollar.

Traders said muted opening in domestic equities, easing crude oil prices and weak dollar supported the local unit.

Meanwhile, the benchmark indices Sensex trading 32.40 points higher at 41,053.01 and Nifty was up 5.80 points at 12,106.50.

The dollar index, which gauges the greenback's strength against a basket of six currencies, fell marginally by 0.03 per cent to 98.33.

Brent crude futures, the global oil benchmark, fell 0.28 per cent to trade at USD 63.88 per barrel.

Foreign institutional investors (FIIs) remained net buyers in the capital market, as they purchased shares worth Rs 42.93 crore on Wednesday, according to provisional exchange data.

The 10-year government bond yield was at 6.47 per cent on Thursday.