The rupee dropped by another 15 paise to 63.73 against the US currency in late morning trade due to sustained dollar demand from banks and importers amid higher dollar overseas.
The rupee resumed lower at 63.65 per dollar as against previous closing of 63.58 at the Interbank Foreign Exchange (Forex) market.
It moved in a range of 63.64 and 63.74 per dollar during morning deals before quoting at 63.73 at 1030hrs.
Banks and importers were increasing their dollar position in view of higher dollar in the overseas market, a forex dealer said.
The dollar index, which tracks the greenback against a basket of major currencies, was down at 97.39 in early trade.
Oil prices were mixed in Asia early trade, with WTI stuck below USD 50 a barrel after a rise in US stockpiles added to concerns over a supply glut, analysts said.
At the New York market, the dollar ended higher against most of its other rivals, after National Association of Realtors reported that US existing-home sales in June grew at the fastest pace since February 2007.
Meanwhile, the benchmark 30-share index was trading up by 16 points or 0.06 per cent to 28,520.74 at 1035hrs.