The rupee depreciated 29 paise to 73.32 against the US dollar in opening trade on Thursday tracking muted domestic equities and strengthening American currency.
At the interbank forex market, the rupee opened on a weak note at 73.23, then fell further to 73.32, registering a fall of 29 paise over its last close.
The rupee depreciated 16 paise to close at 73.03 against the US dollar on Wednesday.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, rose 0.07 per cent to 92.91.
Forex traders said strong dollar and muted domestic equities weighed on investor sentiment. However, sustained foreign fund inflows supported the rupee and restricted the decline.
On the domestic equity market front, the 30-share BSE benchmark Sensex was trading 71.54 points higher at 39,157.57 and broader NSE Nifty gained 30 points to 11,565.00.
Foreign institutional investors were net buyers in the capital market as they purchased shares worth Rs 990.57 crore on Wednesday, according to provisional exchange data.
Brent crude futures, the global oil benchmark, fell 0.07 per cent to $44.40 per barrel.
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