Negative closing in Indian stocks and a firm dollar overseas, however, restricted the rupee's rise.
The Indian rupee opened higher at 61.84 a US 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 US 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.
In three trading days, the Indian rupee has shot up by 35 paise or 0.56 per cent against the US dollar.
The BSE benchmark Sensex today washed out initial gains and closed down by 68.32 points, or 0.32 per cent.
As per provisional data, FIIs pumped in Rs 40.67 crore today in stocks. Yesterday, net inflows was Rs 135.42 crore.
The US 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.
Pramit Brahmbhatt, CEO, Alpari Financial Services (India) said: "Today US dollar index, which tracks the performance of the greenback versus a basket of six major currencies, traded positive as most of the investors are waiting for new year 2014 to open their new books of accounts.
"Indian 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."
"Indian rupee has retraced all of the pre-FOMC loses and is now trading at a week's high. However, action is expected to be muted as we approach the end of the year.
"We expect a range of 61.00/50 and 62.50/63.00 for the next couple of weeks," Anindya Banerjee, currency analyst, Kotak Securities.
Forward US dollar premiums rebounded on fresh payments from banks and corporates.
The benchmark six-month forward dollar premium payable in May rose to 232-234 paise from 227-1/2-229-1/2 paise previously.
Far-forward contracts maturing in November also recovered to 474-476 paise from 465-1/2-467-1/2 paise.
The RBI fixed the reference rate for the dollar at 61.8668 and for the euro at 84.6510.
The Indian rupee improved further against the pound to 101.13 from 101.32 yesterday while it recovered to 84.49 per euro from 84.75.
The Indian rupee bounced back to 59.25 per 100 Japanese yen from 59.66.