The rupee plunged 32 paise to close at an all-time low of 81.94 (provisional) against the US dollar on Thursday amid high volatility as firm crude oil prices weighed on the local unit.

At the interbank foreign exchange market, the local currency opened on a positive note at 81.52, then pared all the gains to settle at an all-time low of 81.94 against the American currency, registering a decline of 32 paise over its previous close.

During the day, the local unit witnessed an intra-day high of 81.51 and a low of 81.94 against the greenback.

On Tuesday, the rupee appreciated by 20 paise to end at 81.62 against the US dollar.

The forex market was closed on Wednesday on account of Dussehra.

"Rupee, after appreciating marginally on Tuesday, is again starting to come under pressure. The dollar strengthened after services PMI and private payrolls numbers from the US came in better than estimates," said Gaurang Somaiya, Forex & Bullion Analyst, Motilal Oswal Financial Services.

Major crosses euro and pound continued to witness selling pressure at higher levels. The focus will be on the European Central Bank (ECB) meeting minutes, Somaiya said.

"We expect the USD/INR (Spot) to quote in the range of 81.20 and 82.05," Somaiya added.

Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, advanced 0.06 per cent to 111.27.

Global oil benchmark Brent crude futures fell 0.08 per cent to USD 93.30 per barrel.

On the domestic equity market front, the 30-share BSE Sensex advanced 156.63 points or 0.27 per cent to end at 58,222.10, while the broader NSE Nifty rose 57.50 points or 0.33 per cent to 17,331.80.

Foreign institutional investors were net buyers in the capital market on Tuesday as they purchased shares worth Rs 1,344.63 crore, as per exchange data.