The rupee depreciated 4 paise to hit an all-time closing low of 83.41 (provisional) against the US dollar on Wednesday amid a strong American currency overseas.

Forex traders said a steep fall in crude oil prices from $76 per barrel to the below $73 level provided support, but a muted trend in equity markets triggered negative bias against the local unit.

At the interbank foreign exchange market, the local unit opened at 83.39 against the greenback and traded in a tight range of 83.38-83.41. It finally settled at its lifetime low of 83.41 (provisional), a fall of 4 paise from the previous close.

On Tuesday, the domestic currency settled at 83.37 against the dollar.

The rupee had earlier recorded its lowest closing level of 83.40 on November 24 this year.

The government data released on Tuesday showed India's retail inflation rose to a three-month high of 5.55 per cent in November, though it remained within the RBI's comfort zone of less than 6 per cent.

Industrial production growth, however, accelerated to a 16-month high of 11.7 per cent in October, mainly due to double-digit growth in manufacturing, power and mining sectors' output, according to the official data.

Forex traders are awaiting the US Federal Reserve's monetary policy decision to be announced on Wednesday.

Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, was trading 0.09 per cent higher at 103.55 on Wednesday.

Brent crude futures, the global oil benchmark, declined 0.38 per cent to $72.96 per barrel.

In the domestic equity market, the 30-share BSE Sensex settled 33.57 points or 0.05 per cent higher at 69,584.60 points. The broader NSE Nifty inched up 19.95 points or 0.01 per cent at 20,926.35 points.

Foreign Institutional Investors (FIIs) were net buyers in the capital market on Tuesday as they bought shares worth ₹76.86 crore, according to exchange data.

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