The domestic currency dipped 6 paise to 75.42 against the US dollar in opening trade on Tuesday.
The Rupee was weighed down by the strengthening of the greenback in the overseas market and firm crude oil prices.
At the interbank foreign exchange, the rupee opened on a weak note at 75.41, then fell further to 75.42, registering a decline of 6 paise from the last close.
In initial deals, the rupee also touched a high of 75.32 against the American currency.
On Monday, the rupee slid by 37 paise to close at a 15-month low of 75.36 against the US dollar on Monday.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, rose 0.03 percent to 94.34.
Global oil benchmark Brent crude futures declined 0.06 per cent to $83.60 per barrel.
"Oil is the main culprit taking USD/INR higher along with US and India yields moving higher. RBI is conspicuous by its absence," said Anil Kumar Bhansali, Head of Treasury, Finrex Treasury Advisors.
Bhansali further added "until oil prices fall or RBI comes and sells dollars, we will not be able to see lower levels." The range for the day 75.30 to 75.80 with risk on the upside, he noted.
Moreover, foreign institutional investors were net sellers in the capital market on Monday as they offloaded shares worth Rs 1,303.22 crore, as per exchange data.
On the domestic equity market front, the 30-share Sensex was trading 37.91 points or 0.06 per cent higher at 60,173.69, while the broader NSE Nifty was trading 12.80 points or 0.07 per cent higher at 17,958.75.
