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The rupee gained 11 paise to 82.68 against the US dollar in early trade on Tuesday as the American currency retreated from its elevated levels.
Forex traders said sustained foreign fund outflows weighed on the local unit and restricted the appreciation bias.
At the interbank foreign exchange, the domestic unit opened at 82.69 against the dollar and marginally rose to 82.68, registering a rise of 11 paise over its previous close amid a positive trend in domestic equities.
On Monday, the rupee closed at 82.79 against the US currency.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, rose 0.06 per cent to 104.73.
"After marking a seven-week high, the DXY pulled back towards 104.60 levels after a higher-than-expected drop in US durable goods orders (measures the change in the total value of new orders for durable manufactured goods)," said Amit Pabari, MD, CR Forex Advisors.
Brent crude futures, the global oil benchmark, advanced 0.17 per cent to $82.59 per barrel.
Forex traders said the rupee is likely to trade with a negative bias on risk aversion in global markets and positive greenback.
Moreover, month-end dollar demand from importers may also weigh on the rupee, they added.
In the domestic equity market, the 30-share BSE Sensex rose 84.34 points or 0.14 per cent to 59,372.69 points.
The broader NSE Nifty advanced 11.15 points or 0.06 per cent to 17,403.85 points.
Foreign Institutional Investors (FIIs) were net sellers in the capital market on Monday as they offloaded shares worth Rs 2,022.52 crore, according to exchange data.