The rupee edges up to 60.95/96 versus its Friday close of 61.19/20, tracking gains in the domestic share market. Financial markets were closed on Monday for a local holiday.
Most other Asian currencies trading stronger compared with the dollar.
Traders will also monitor the domestic share market for cues on foreign fund flows.
The euro edged up 0.1% to $1.3934, within reach of a 2-1/2-year high around $1.3967 hit on Thursday on diminished expectations of easing by the European Central Bank.
Traders expect importers to buy the greenback around 60.85-90 levels holding the USD/INR pair in a 60.80 to 61.20 range for the session.