Dollar's stability in overseas markets and a decline in capital inflows, however, capped the rupee rise, a forex dealer said.
At the Interbank Foreign Exchange (Forex) market, the domestic unit swung between 61.76 and 62.02. It settled at 61.81, a rise of 7 paise from its previous close.
"Rupee traded range-bound today but managed to close slightly strong after a three-day fall. Local equities posted its record high closing today, supporting the rupee movement," said Pramit Brahmbhatt, CEO, Alpari Financial Services (India).
The dollar index was trading nearly flat against its major global rivals.
"After trading in a tight range for almost a week, rupee has finally come out and started its firm trend against the US dollar....Next couple of days' closing will be closely watched to get the further direction of the pair,"said Abhishek Goenka, Founder and CEO, India Forex Advisors.
Forward dollar premiums ended better on fresh payments from banks and corporates.
Far-forward contracts maturing in December improved further to 448.5-450.5 paise from 443.5-445.5 paise.
The RBI fixed the reference rate for the dollar at 61.92 and for the euro at 83.9267.
The rupee remained weak to settle at 102.27 against the pound from last close of 101.62. It declined further to 83.76 per euro from 83.72. The local currency also fell back to 59.24 per 100 Japanese yen from 59.13.
