Risk aversion sentiment among investors ahead of the US Federal Reserve's interest rate decision also impacted trading, forex dealers said.
At the interbank foreign exchange market, the rupee opened lower at 82.63 against the greenback and witnessed a high of 82.60 and a low of 82.87.
It finally settled at 82.87, down 36 paise over its previous close of 82.51.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, fell 0.15 per cent to 104.98.
Brent crude futures, the global oil benchmark, climbed 1.73 per cent to USD 79.32 per barrel.
In the domestic equity market, the 30-share BSE Sensex closed 402.73 points or 0.65 per cent higher at 62,533.30. The broader NSE Nifty rose 110.85 points or 0.60 per cent to 18,608.
Foreign Institutional Investors (FIIs) remained net sellers in the capital markets on Monday as they offloaded shares worth Rs 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.
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