Indian rupee depreciated 29 paise to 73.64 per dollar in Tuesday's opening deals amid rise in demand for the US currency from banks and importers.
Forex traders said strengthening American currency and foreign fund outflows weighed on the local unit.
The Indian currency started off on a tepid note at 73.63 at the interbank forex market, then fell further to 73.64 against the greenback, down 29 paise over its previous close of 73.35 against the US dollar.
The local unit traded in a narrow band of 73.54-73.64 per US dollar in early trade.
"US markets were shut on account of Labour Day and therefore there are no overnight cues to follow. We are seeing the US nominal yields firm up and we are seeing US dollar strength in pockets," said Abhishek Goenka Founder and CEO, IFA Global.
Goenka further said that "if the broader USD remains stable, the down side in USD-INR could be limited. It appears the central bank is content keeping volatility in check and allowing readjustments in USD-INR happen when there is a significant global USD move".
The dollar index, which gauges the greenback's strength against a basket of six currencies, rose 0.44% to 93.12.
On the domestic equity market front, market benchmarks traded on a bullish note on Tuesday, amid positive global equities. Sensex traded 250 points higher at 38,668 and Nifty gained 72 points to 11,427.
Foreign portfolio investors (FPIs) sold shares worth Rs 6.93 crore, while domestic institutional investors (DIIs), were net sellers to the tune of Rs 815.82 crore in the Indian equity market on 7 September, provisional data showed.
Oil price fell as Saudi Arabia made the deepest monthly price cuts for supply to Asia even as demand recovery expectation during the pandemic cooled. Brent crude futures, the global oil benchmark, fell 0.12 per cent to USD 41.96 per barrel.
Worldwide, there were 274 lakh confirmed cases and 8.96 lakh deaths from COVID-19 outbreak. Meanwhile, India's death toll from COVID-19 infections rose to 72,816 and total coronavirus cases to 42.80 lakh as of Tuesday.