The local unit opened at 74.40 at the interbank forex market, down 30 paise over its last close.
On Thursday, the rupee had declined further by 23 paise to close at a two-month low of 74.10 against the US currency.
Forex market was closed on Friday on account of Id-E-Milad.
Losses in domestic stock markets and uncertainty ahead of US presidential election weighed on the investor sentiment, traders said.
"We may continue to see bids in USD/INR on account of overall global risk aversion. 74.95 is an extremely crucial resistance. 73.65 is now likely to act as a support. We expect an intraday range of 74.25-74.65," said Abhishek Goenka, Founder and CEO, IFA Global.
Goenka further added that "we have the US presidential election on November 3rd (Tuesday), Reserve Bank of Australia rate decision on Tuesday, Bank of England on Thursday
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, rose 0.13 per cent to 94.15.
On the domestic equity market front, the 30-share BSE benchmark Sensex was trading 129.29 points lower at 39,484.78 and the broader NSE Nifty fell 40.45 points to 11,601.95.
Foreign institutional investors were net sellers in the capital market as they offloaded shares worth Rs 870.88 crore on a net basis on Friday, according to provisional exchange data.
Brent crude futures, the global oil benchmark, fell 3.22 per cent to USD 36.72 per barrel.