The rupee appreciated 12 paise to 74.88 against the US dollar in opening trade on Tuesday, tracking gains in domestic equity markets.
At the interbank foreign exchange, the rupee opened strong at 74.95 against the American dollar, then inched higher to 74.88, registering a rise of 12 paise from the last close.
The rupee on Monday appreciated 3 paise to nearly four-week high of 75 against the US dollar.
Positive moves in Indian equity indices and stronger Asian currencies aided sentiments, forex traders said, adding that trading is likely to remain range-bound this week ahead of the year-end holidays.
Moreover, Omicron worries and firm crude oil prices contained the appreciation bias in the local unit, they added.
The dollar index, which gauges the greenback's strength against a basket of six currencies, was trading unchanged at 96.09.
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Meanwhile, on the domestic equity market front, the 30-share Sensex was trading 369.58 points or 0.64 per cent higher at 57,789.82, while the broader NSE Nifty advanced 115.30 points or 0.67 per cent to 17,201.55.
Global oil benchmark Brent crude futures rose 0.18 per cent to USD 78.74 per barrel.
Foreign institutional investors remained net sellers in the capital market on Monday, as they offloaded shares worth Rs 1,038.25 crore, as per exchange data.
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