The rupee touched a high and low of 65.91 agaisnt the greenback during the day.
The Reserve Bank of India today fixed the reference rate of the rupee at 65.96 against the US dollar and 73.37 for the euro as against 65.62 and 73.26, respectively, yesterday.
According to an RBI statement, the exchange rates for the pound and the yen against the rupee were quoted at 101.19 and 54.92 per 100 yens, respectively, based on reference rates for the dollar and cross-currency quotes at noon.
The SDR-rupee rate will be based on this rate, the statement added.
The rupee had ended 15 paise lower at 65.88 on Tuesday on sustained demand for the American currency from banks and importers amid a big fall in domestic equities.
Meanwhile, tracking firm European cues, Indian shares today snapped their two-day losing streak as the market benchmark Sensex ended 171.15 points higher at 25,822.99 driven by short covering in recently beaten-down stocks of realty and banking sectors.
Some value-buying in index majors ahead of September derivatives expiry also triggered the rebound.