The rupee gained 14 paise to 81.67 against the US dollar in early trade on Tuesday tracking the weakness of the American currency in the overseas market.
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 81.74, then touched a high of 81.67 against the American currency, registering a rise of 14 paise over its last close.
On Monday, the rupee had settled at 81.81 against the dollar.
"The flows have been strong enough and despite buying by RBI at various levels has kept the rupee on the stronger side despite a rise in dollar index to 101.30," said Anil Kumar Bhansali, Head of Treasury and Executive Director, Finrex Treasury Advisors LLP.
The dollar index fell 0.09 per cent to 101.25.
Brent crude futures, the global oil benchmark, rose 0.18 per cent to $82.89 per barrel.
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Participants in the rupee and dollar markets are eagerly awaiting cues from the US Federal Reserve's monetary policy meetings this week, traders said.
"The US Fed is expected to raise rates by 25 bps tomorrow but their language/ tone will be important in gauging the direction currencies could take," Bhansali said.
In the domestic equity market, BSE Sensex was trading 1.77 points higher at 66,386.55. NSE Nifty advanced 4.40 points or 0.02 per cent to 19,676.75.
Foreign Institutional Investors (FIIs) were net sellers in the capital markets on Monday as they offloaded shares worth ₹82.96 crore, according to exchange data.