The rupee depreciated 12 paise to 81.64 against the US dollar in early trade on Tuesday, weighed down by significant foreign fund outflows and a muted trend in domestic equities.
At the interbank foreign exchange, the domestic unit opened weak at 81.61 against the dollar, then lost ground and fell to 81.64, registering a decline of 12 paise over its last close.
In the previous session on Monday, the rupee settled at 81.52 against the American currency.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, fell 0.04 per cent to 102.23.
Brent crude futures, the global oil benchmark, advanced 0.02 per cent to USD 84.92 per barrel.
Forex traders said the rupee is likely to witness range-bound trading as investors brace for interest rate decisions from the Federal Reserve, and the Union Budget for 2023-24, both scheduled to be announced on Wednesday.
Meanwhile, the Budget session of Parliament kicks off on Tuesday. The session will commence with the maiden address of President Droupadi Murmu to the joint sitting of both Houses of Parliament.
The Economic Survey will be also tabled on Tuesday after the President's address.
In the domestic equity market, the 30-share BSE Sensex was trading 190.52 points or 0.32 per cent lower at 59,309.89. The broader NSE Nifty declined 60.25 points or 0.34 per cent to 17,588.70.
Foreign Institutional Investors (FIIs) were net sellers in the capital markets on Monday as they offloaded shares worth Rs 6,792.80 crore, according to exchange data.