The rupee is trading at 61.41/42 versus its close of 61.46/47, helped by gains in the domestic share market with sentiment cautious ahead of the Reserve Bank of India's policy review on Tuesday.
All Asian currencies trading stronger versus the dollar.
The BSE Sensex is trading up 0.4 percent.
The dollar licked its wounds in early Asian trading on Monday, steadying against major counterparts ahead of the U.S. Federal Reserve's policy-setting meeting following a testing week which saw it tumble to two-year lows against the euro.
The RBI will also release its macroeconomic policy review in the evening on Monday, which will be eyed for opening cues on Tuesday.