However, persistent foreign capital inflows into equity market restricted the rupee's fall against the dollar, a forex dealer said.
The Indian rupee resumed higher at 60.05 per dollar as against the last closing level of 60.14 at the Interbank Foreign Exchange market on initial selling of dollars by some banks.
However, it declined immediately to 60.30 per dollar on fresh dollar demand from banks and importers before quoting at 60.28 at 1000 hours.
It hovered in a range of 60.05-60.30 per dollar during the morning deals.
However, in New York market, the dollar fell further against the euro yesterday after minutes from the Federal Reserve's March meeting detailed risks that could keep interest rates depressed even after the first rate hike.
Meanwhile, BSE Sensex rose to an all-time high of 22,792.49 before quoting at 22,721.78 at 1000 hours, showing a rise of 19.44 points, or 0.09 per cent, from its last close.