Negative closing in Indian stocks and a firm dollar overseas, however, restricted the rupee's rise.
The rupee opened higher at 61.84 a dollar from yesterday's close of 61.95 at the Interbank Foreign Exchange market. However, it fell back in afternoon trade to a low of 61.97 tracking a drop in stocks and a strong dollar abroad.
Later, it bounced back on dollar selling by exporters and some banks to a high of 61.78, before settling at 61.79, a net rise of 16 paise or 0.23 per cent. This is its best closing since 61.73 on December 16.
The BSE benchmark Sensex today washed out initial gains and closed down by 68.32 points, or 0.32 per cent.
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As per provisional data, FIIs pumped in Rs 40.67 crore today in stocks. Yesterday, net inflows was Rs 135.42 crore.
The dollar index was last trading up by 0.12 per cent against a basket of six major global currencies amid low volumes due to a holiday-shortened week. Later in the day, orders for durable goods in November are expected to be out.
"Rupee continued to trade strong for the third day in a row and appreciated...Immediate support for USD/INR spot is at 61.50. The trading range for the USD/INR is expected to be within 61.50 to 62.50.