The partially convertible rupee closed at 61.845/855 versus Monday's close of 62.04/05 per dollar.
The gains in emerging market currencies came 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.
Any resurgence in global risk aversion threatens to reverse the strong dollar inflows into local stocks and debt, which totalled more than $2 billion in February, and helped push the rupee to its highest in more than a month on Friday.
With no major trigger, the rupee is largely expected to trade rangebound ahead of general elections due by May.
The economy, however, continues to be a matter of concern as contracting industrial output and an investment slowdown dragged India's economic growth to a worse-than-expected 4.7 percent in the three months to December.
In the offshore non-deliverable forwards, the one-month contract was at 62.25 while the three-month was at 62.98.