The rupee depreciated 20 paise to 82.71 against the US dollar in early trade on Tuesday due to unabated foreign fund outflows from domestic capital markets.
However, a positive trend in equity markets and a weak dollar overseas capped the rupee's fall, forex traders said.
Investors remained in risk-off mode ahead of the US inflation data release and Federal Reserve decision on interest rates slated to be announced later this week, they added.
At the interbank foreign exchange, the domestic unit opened weak at 82.63 against the dollar, then lost further ground to 82.71, registering a decline of 20 paise over its previous close.
In the previous session, the rupee fell 23 paise to end at 82.51 against the US dollar.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, fell 0.16 per cent to 104.96.
Brent crude futures, the global oil benchmark, advanced 1.23 per cent to $78.95 per barrel.
In the domestic equity market, the 30-share BSE Sensex was trading 115.85 points or 0.19 per cent higher at 62,246.42. The broader NSE Nifty rose 23.45 points or 0.19 per cent to 18,520.60.
Foreign Institutional Investors (FIIs) remained net sellers in the capital markets on Monday as they offloaded shares worth ₹138.81 crore, according to exchange data.
Meanwhile, retail inflation dipped below the RBI's upper tolerance level of 6 per cent for the first time in 11 months in November as softening prices of food items brought relief but the central bank may wait for more data before pausing hikes in interest rates.
As per the data released by the National Statistical Office (NSO) on Monday, the consumer price index (CPI) based inflation declined for the second consecutive month to 5.88 per cent in November, from 6.77 per cent in October 2022. It was 4.91 per cent in November last year.
India's industrial production contracted by 4 per cent in October, the sharpest fall in 26 months, mainly due to a decline in output of manufacturing and subdued performance of mining and power generation sectors, according to official data released on Monday.