The rupee is trading weaker at 61.97/98 versus its close of 61.79/80 on Tuesday, with dollar demand from oil firms hurting.
Traders expect exporters to step up dollar selling around 62-62.05 levels, limiting very sharp gains from current levels.
The Thai baht hit a near four-year low on Thursday, pressured by political uncertainty, while most emerging Asian currencies eased in holiday-thinned trading on expectations that a solid US economic recovery would allow the Federal Reserve to gradually withdraw its stimulus.
The Sensex is trading up 0.2% while the broader Nifty is up 0.24%.