The rupee resumed marginally higher at 55.60 per dollar as against the last closing level of 55.63, but fell sharply to 55.74 on good demand for the American currency from banks and importers.
However, it recovered to 55.57 on mild selling of dollars before quoting at 55.62 at 1040hrs.
In New York, the dollar index climbed to its highest level in about two years yesterday.
Meanwhile, the BSE 30-stock benchmark Sensex fell by 178 points or 1.02 per cent at 1050hrs.