The rupee on Monday fell by 17 paise to touch a fresh two-month low of 54.78 against the dollar in early trade at the Interbank Foreign Exchange, due to increased demand for the American currency from oil importers.

Besides, euro's weakness against the dollar overseas on renewed worries about Greece's debt crisis and US presidential elections also put pressure on the local unit, forex dealers said.

The rupee had plunged by 80 paise on Monday to close at over eight-week low of 54.61 on massive dollar demand from banks and importers amid a sharp rise in the American currency overseas.

Meanwhile, the BSE benchmark Sensex rose by 48.09 points, or 0.25%, to 18,810.96 in early trade on Tuesday.