Traders are keenly awaiting the allotment of cabinet portfolios.
The pair is seen holding in a 58.30 to 58.60 range during the session.
The BSE Sensex is trading up 1.3 percent.
Gains in other Asian currencies versus the dollar also likely to hurt the pair.
Traders will, however, remain watchful of RBI intervention to buy dollars in case the pair slips sharply.