Traders said dollar demand from banks and importers on the back of higher dollar in overseas market put the currency under pressure.
It moved in a range of 55.13 per dollar and 55.37 per dollar during the morning deals.
"The rupee is still expected to be weak with some dips in between," said forex advisors in a report.
In New York, the dollar turned higher on Tuesday as attention shifted back toward whether and when Greece will get its next installment of bailout funds.
Meanwhile, BSE Sensex rose by 80.13 points, or 0.44%, to 18,409.45 at 1100 hrs.