The rupee gained 6 paise to 82.11 against the US dollar in early trade on Monday 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 82.14, then touched a high of 82.11 against the American currency, registering a rise of 6 paise over its last close.
On Friday, the rupee had settled at 82.17 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.
The dollar index, which gauges the greenback's strength against a basket of six currencies, rose 0.05 per cent to 99.96.
Brent crude futures, the global oil benchmark, rose 0.85 per cent to $79.19 per barrel.
In the domestic equity market, the 30-share BSE Sensex was trading 33.35 points or 0.05 per cent higher at 66,094.25. The broader NSE Nifty advanced 22.55 points or 0.12 per cent to 19,587.05.
Foreign Institutional Investors (FIIs) were net buyers in the capital markets on Friday as they purchased shares worth Rs 2,636.43 crore, according to exchange data.
Meanwhile, India's foreign exchange reserves jumped $1.229 billion to $596.28 billion in the week ended July 7, the Reserve Bank of India said on Friday.
In the previous week, the overall forex reserves increased $1.85 billion to $595.05 billion.