The rupee opened weak at 71.45 at the interbank forex market and then fell further to 71.47, down 10 paise over its last close.
The rupee had settled at 71.37 against the US dollar on Friday.
Meanwhile, easing crude prices supported the local unit and restricted the fall.
Brent crude futures, the global oil benchmark, fell 0.19 per cent to USD 57.21 per barrel.
Foreign institutional investors (FIIs) remained net sellers in the capital markets, pulling out Rs 704.92 crore on Friday, as per provisional data.
The BSE Sensex was trading 65 points, or 0.16 per cent, lower at 41,192.74.
Likewise, the NSE Nifty was trading down by 28 points, or 0.23 per cent, at 12,085.45.
The dollar index, which gauges the greenback’s strength against a basket of six currencies, fell marginally by 0.01 per cent to 99.11.
The 10-year government bond yield was at 6.36 per cent in the morning trade.