The rupee depreciated 7 paise to 79.33 against the US dollar in early trade on Monday as a muted trend in domestic equities and risk-averse sentiments weighed on the local unit.
However, sliding crude prices in the international market restricted the rupee's fall, according to forex traders.
At the interbank foreign exchange, the rupee opened weak at 79.30 against the American dollar and slipped further to quote at 79.33, a decline of 7 paise over its last close.
In initial trade, the local currency witnessed a high of 79.24 and a low of 79.35 against the US dollar.
In the previous session, the rupee had closed at an all-time low of 79.26 against the dollar.
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On the domestic equity front, the 30-share Sensex was trading 265.1 points or 0.49 per cent lower at 54,216.74, while the broader NSE Nifty slipped 89.80 points or 0.55 per cent to 16,130.80.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, gained 0.31 per cent to 107.34.
Global oil benchmark Brent crude futures declined 0.63 per cent to $106.35 per barrel.
Foreign institutional investors were net sellers in the capital market on Friday as they sold shares worth Rs 109.31 crore, as per exchange data.
Foreign investors continue to desert Indian equity markets and have pulled out over Rs 4,000 crore this month so far amid steady appreciation of the dollar and rising interest rates in the US.
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However, the pace of selling by foreign portfolio investors (FPIs) has been declining over the last few weeks.
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