The rupee is trading at 61.75 vs Monday's close of 61.73/74.
Custodian banks seen selling dollars.
The Indian unit earlier hit one-month low of 61.8750 on dollar buying by oil firms.
Index of the dollar versus six majors down 0.25 pct.
Investors awaiting this week minutes of U.S. Fed's policy meeting.
The 50-share Nifty almost flat, after earlier gaining as much as 0.28 percent to touch a record high.
(Reporting by Gaurav Pai)
