The rupee resumed lower at 51.37/38 per dollar at the Interbank Foreign Exchange (Forex) market as against last Wednesday's closing level of 51.11/12 per dollar and declined further to 51.45. It was at 51.31/32 per dollar at 1030 hrs.
It hovered at 51.20-51.45 against the dollar during the morning deals.
Forex dealers said that strong demand for the American currency from importers, some banks and oil refiners amid weakness in local equities markets impacted the rupee value against the dollar.
The BSE 30-scrip Sensex lost 221.71 points, or 1.27 per cent, at 17,264.31 in early trade.
In New York, the US dollar dropped against other major currencies on Friday after the government data triggered worries about America's labour market and economic recovery.
The forex and money markets in India were closed on Thursday and Friday, followed by the weekend for public holidays.