In early trade on Tuesday, the rupee fell 18 paise to 74.43 against the US dollar, as investor sentiment was influenced by a stronger US dollar and higher crude oil prices.
The slowdown in the domestic equity market, as well as dollar purchases by banks from importers, added to the pressure on the local currency, according to forex traders.
The rupee opened weak against the US dollar in the interbank foreign exchange market, at 74.36, before falling to 74.43, a drop of 18 paise from the previous closing price.
The rupee fell 10 paise to 74.25 against the USdollar on Monday.
Meanwhile, the dollar index, which measures the value of the US dollar against six major currencies, increased by 0.11 percent to 95.36.
Brent crude futures were up 0.94 percent at $87.29 per barrel, the international benchmark.
According to provisional data from the stock market, foreign institutional investors (FIIs) sold shares worth Rs 855.47 crore on a gross basis on Monday.