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, which gauges the greenback's strength against a basket of six currencies, rose 0.14 per cent to 102.16.
Brent crude futures, the global oil benchmark, fell 0.07 per cent to USD 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
In the domestic equity market, the 30-share
Meanwhile, India's forex reserves dropped by USD 3.165 billion to USD 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 USD 1.987 billion decline to USD 607.035 billion in the previous week.