The rupee is trading at 59.39/40 versus its previous close of 59.3850/3950, tracking largely mixed Asian currencies with traders watching the domestic sharemarket for clues on foreign fund flows.
Traders expect the rupee to remain in a range until the government unveils its budget, likely in early or mid-July.
The pair is expected to hold in a broad 59.20 to 59.60 range this week.
The BSE Sensex was trading 0.2% lower.