The rupee was trading in a narrow range against the US dollar in the morning session on Tuesday amid a weak American currency and a muted trend in domestic equities.

Forex traders said foreign fund outflows also weighed on the local unit.

At the interbank foreign exchange, the rupee opened at 81.95 against the dollar. It touched a high of 81.86 in initial deals.

The rupee on Monday settled at 81.92 against the US dollar.

Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, was trading at 101.33, down 0.02 per cent.

Global oil benchmark Brent crude futures declined 0.01 per cent to USD 82.72 per barrel.

On the domestic equity market front, BSE Sensex was trading 4.41 points or 0.01 per cent lower at 60,051.69 points while the broader NSE Nifty declined 2.40 points or 0.01 per cent to 17,741.00 points.

Foreign institutional investors were net sellers in the capital market on Monday as they offloaded shares worth Rs 412.27 crore, as per exchange data.

"Rupee will remain between the levels of 81.80 to 82.20 as RBI buys dollars at lower levels and inflows continue at higher levels to keep it well boxed in the small range for the moment," Anil Kumar Bhansali, Head of Treasury at Finrex Treasury Advisors LLP, said.

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