The Reserve Bank of India was spotted buying dollars via state-run banks starting around 58.47, which was the rupee's strongest level in 11 months, three traders said.
The rupee trading at 58.52/53 per dollar by 0359 GMT, off its session high of 58.47, its highest since June 18. The currency closed at 58.79/80 on Friday.
The rupee had gained at open on expectations of continued robust foreign buying in domestic shares and debt after the Bharatiya Janata Party swept the country's elections.
A trader with a brokerage expects the USD/INR pair to be in a 58.50 to 58.70 range during the session.