The rupee rose to 61.91/92 against the dollar versus Monday's close of 62.04/05, after falling to 62.15 in early sessions.
Most emerging Asian currencies turned higher on Tuesday after Russia's president ordered troops in military drills in central and western Russia to return to base, increasing hopes of a peaceful solution in Ukraine.
The BSE Sensex ended up more than 1%.
Some bids were seen from large state-run bank at current levels.