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Dollar losses against the euro and other major currencies overseas also supported the gains.
The rupee had depreciated by 3 paise to close at Rs 44.51/52 against the US dollar in the previous session.
Dealers said steady capital inflows and the higher opening in the stock market mainly kept the rupee sentiment firm.
The Bombay Stock Exchange benchmark Sensex moved up by 88.28 points, or 0.45 per cent, to 19,633.63 in opening trade today.