The depreciated 10 paise to 81.69 against the early trading on Monday was weighed down by foreign fund outflows.
The domestic unit opened weak against the dollar at the interbank foreign exchange, registering a decline of 10 paise over its last close.
The previous session on Friday settled at 81.59 against the American currency.
The dollar index, which measures the dollar's strength against a basket of six currencies, fell by 0.01 per cent to 101.92.
Brent crude futures, the global oil benchmark, declined by 0.17 per cent to USD 86.51 per barrel.
The focus on the US Federal Reserve and the Union Budget will determine the course for the local unit on Monday, traders said.
Asian and emerging market peers have started with gains that could aid investor sentiments. Sriram Iyer, Senior Research Analyst at Reliance Securities said that demand from India's Reserve Bank and the Reserve Bank of India's presence could cap gains.
India's forex reserves increased by USD 1.727 billion in the week ended January 20, to USD 573.727 billion, according to the RBI on Friday. This is the second week in a row of rise in the kitty.
In the domestic equity market, the 30.72 points or 0.05 per cent increased the BSE Sensex by 30.72 points or 59,361. The NSE Nifty grew 17.55 points or 0.1 per cent to 17,621. Foreign Institutional Investors FIIs turned net sellers in the capital markets on Friday as they offloaded shares worth Rs 5,977. According to exchange data, 86 crore were lost due to a selloff by the Adani Group on Friday.