The rupee opened sharply lower at 65.88 as against last Friday's level of 65.67 at the Interbank Foreign Exchange (forex) market.
It moved in a range of 65.88 and 65.77 during the morning deals before quoting at 65.80 at 1030 hours.
The dollar index is currently trading down by 0.15 per cent at 95.09 as against a basket of six currencies.
"The overnight equity sell-off will keep sentiment slightly weak. Dollar demand would come in from importers on dips to 65.55-65.60 per dollar. Any uptick towards 66 per dollar will see some exporter selling to hedge their receivables, a dealer said.
Oil prices rebounded in Asia trade, but analysts said they remain weighed down by an oversupply and fresh worries about the world economy after the Federal Reserve decided last week against raising interest rates.
Meanwhile, the benchmark BSE Sensex was trading lower by 95.04 points at 26,123.87 at 1057 hours.