Dealers said the dollar's weakness against other currencies overseas -- except the Japanese yen -- and a stronger opening in the domestic stock market gave the rupee strength.
Yesterday, the rupee had ended 4 paise lower at 64.19, the second straight session loss against the US currency, owing to bouts of month-end dollar demand from importers and corporates.
Meanwhile, the benchmark Nifty touched a new high of 10,101.05 and the Sensex climbed 100.51 points, or 0.30 per cent, to 32,615.45 in opening trade.