The rupee gained 10 paise to 82.71 against the U.S. dollar in early trade on Monday tracking positive domestic equities.
However, sustained foreign fund outflows and strength of the American currency in the overseas market dented investor sentiments, forex traders said.
At the interbank foreign exchange, the domestic unit opened at 82.73, then touched a high of 82.71 against the American currency, registering a rise of 10 paise over its last close.
On Friday, the rupee had settled at 82.81 against the dollar.
The dollar index rose 0.14 per cent to 102.16.
Brent crude futures, the global oil benchmark, fell 0.07 per cent to $86.18 per barrel.
The RBI monetary policy announcement on Thursday is the key event this week, IFA Global Research Academy said in a note adding that the rupee is likely to trade in the 82.50-82.80 range with sideways price action.
The RBI Governor-headed six-member Monetary Policy Committee's (MPC) meeting is scheduled for August 8-10. The policy decision will be announced on August 10 by Governor Shaktikanta Das.
In the domestic equity market, BSE Sensex was trading 133.11 points or 0.20 per cent higher at 65,854.36. NSE Nifty advanced 41.60 points or 0.21% to 19,558.60.
Foreign Institutional Investors (FIIs) were net sellers in the capital markets on Friday as they offloaded shares worth ₹556.32 crore, according to exchange data.
Meanwhile, India's forex reserves dropped by $3.165 billion to $603.87 billion in the week ended July 28, the RBI said on Friday.
This is the second consecutive weekly drop in the reserves after the $1.987 billion decline to $607.035 billion in the previous week.