Traders said foreign fund outflows and cautious opening in domestic equities weighed on the local unit.
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The rupee appreciated marginally by 9 paise to 68.73 against the US dollar in opening trade Thursday, driven by weakening of the US dollar vis-a-vis other currencies overseas.
Forex traders said the local unit rose tracking gains in other Asian peers. Moreover, selling of the American currency by exporters also supported the domestic unit.
The rupee opened strong at 68.76 at the interbank forex market then gained further ground to touch 68.73 per dollar, displaying gains of 9 paise over its last close.
On Wednesday, the rupee had settled at 68.82 against the US dollar.
The dollar index, which gauges the greenback's strength against a basket of six currencies, fell 0.14 per cent to 97.09.
Foreign investors sold shares worth Rs 16.97 crore on a net basis Wednesday, provisional data showed.
The benchmark BSE Sensex was trading 89.84 points, or 0.23 per cent down to quote at 39,125.80 while the NSE Nifty was trading at 11,652.75, down 34.75 points, or 0.30 per cent.
Meanwhile, brent crude, the global benchmark, was trading at 63.84 per barrel higher by 0.29 per cent.