The rupee gained 6 paise to 82.02 against the US dollar in early trade on Thursday supported by steady foreign fund inflows.
However, a surge in crude oil prices capped sharp gains for the local unit, forex traders said.
At the interbank foreign exchange, the domestic unit opened at 82.05, then touched a high of 82.02 against the American currency, registering a rise of 6 paise over its last close.
On Wednesday, the rupee had settled at 82.08 against the dollar.
Softness in the US dollar and sustained FII inflows supported the rupee, forex traders said, adding that the strength in crude oil prices remains a concern for the local unit, as a sharp surge in prices could limit its gains.
Participants in the rupee and dollar markets are eagerly awaiting cues from the upcoming Federal Reserve rate decision next week, traders said.
The dollar index, which gauges the greenback's strength against a basket of six currencies, fell 0.22 per cent to 100.06.
Brent crude futures, the global oil benchmark, rose 0.13 per cent to USD 79.56 per barrel.
In the domestic equity market, the 30-share BSE Sensex was trading 49.46 points or 0.07 per cent lower at 67,047.98. The broader NSE Nifty declined 13.45 points or 0.07 per cent to 19,819.70.
Foreign Institutional Investors (FIIs) were net buyers in the capital markets on Wednesday as they purchased shares worth Rs 1,165.47 crore, according to exchange data.
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