The rupee fell 13 paise to 79.58 against the US dollar in early trade on Tuesday as strong American currency overseas and losses in domestic equities weighed on investor sentiments.
Besides, persistent foreign fund outflows and elevated crude oil prices kept the pressure on the local unit, forex traders said.
At the interbank foreign exchange, the rupee opened lower at 79.55 against the American dollar and slipped further to quote at 79.58, a decline of 13 paise over its last close.
In initial trade, the local currency witnessed a high of 79.55 and a low of 79.62 against the US dollar.
In the previous session, the rupee had closed at an all-time low of 79.45 against the greenback.
On the domestic equity front, the 30-share Sensex was trading 259.08 points or 0.48 per cent lower at 54,136.15, while the broader NSE Nifty slipped 83.25 points or 0.51 per cent to 16,132.75.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, gained 0.27 per cent to 108.31.
Global oil benchmark Brent crude futures declined 1.48 per cent to $105.52 per barrel.
Foreign institutional investors were net sellers in the capital market on Monday as they sold shares worth Rs 170.51 crore, as per exchange data.
The Reserve Bank on Monday asked banks to put in place additional arrangements for export and import transactions in Indian rupee in view of the increasing interest of the global trading community in the domestic currency.