Weak dollar overseas and selling of the American currency by exporters kept the rupee upbeat, said forex traders.
As per provisional stock exchange level data, FIIs pumped in over Rs 2,500 crore in stocks today.
At the Interbank Foreign Exchange (Forex) market, the rupee commenced strong at 61.01 a dollar from the previous close of 61.11. It moved up to a high of 60.94, before falling back to a low of 61.17 on some dollar demand from importers.
Later, the rupee recovered and closed at 61.07, showing a rise of four paise or 0.07 per cent. This is its strongest level at closing since 61.04 on December 10, 2013.
For the week, it gained 68 paise -- the best gain since the week ending December 6, 2013 when it was up 103 paise.
The benchmark S&P BSE Sensex today shot up by almost 406 points, or 1.89 per cent, to end at a new peak.
The dollar index, a gauge of six major global rivals, was down by 0.12 per cent ahead of key economic data in the US.
Pramit Brahmbhatt, CEO, Alpari Financial Services, India said: "Indian equities closed at all time high almost 2 per cent up for the day mainly supported by the foreign money. Taking cues from this, rupee appreciated but towards the end it lost its way. However, it still managed to end on a positive note. The trading range for the rupee is expected to be within 60.50 to 61.50."
India's current account deficit (CAD) will be contained at less than USD 40 billion this financial year, well below the record level in 2012-13, Finance Minister P Chidambaram said today.
"Weakness in US dollar, sharp rally in local stock markets and strong gains in the euro were seen supporting the positive sentiments in the rupee. Consistent buying by FIIs was further seen adding to gains in the domestic currency. Today's Non Farm Payroll data from the US will be very significant," said Abhishek Goenka, CEO, India Forex Advisors.
Meanwhile, forward dollar premium remained weak on sustained receipts by exporters.
The benchmark six-month premium payable in August moved down further to 250.5-252.5 paise from 252-254 paise. Far forward contracts maturing in February 2015 also declined to 491-493 paise from 495-497 paise previously.
The RBI fixed the reference rate for dollar at 60.9850 and for the euro at 84.5255.
The rupee fell back against the pound to 102.40 from 102.12 and also tumbled to 84.95 per euro from 83.97. It, however, improved further to 59.33 per 100 Japanese yen from 59.51.