Besides, a weak dollar against major world currencies globally after the Federal Reserve signalled it will move gradually once it starts tightening policy, supported the domestic unit.
The rupee resumed higher at 63.68 as against previous closing level of 63.73 at the Interbank Foreign Exchange (Forex) but eased temporarily to 63.86 in late trade.
The domestic currency finally settled at one month-high of 63.55, a rise of 18 paise, or 0.28 per cent.
India Forex Advisors said that the rupee is expected to trade in 63.40-64.50 range in the short term. "Importers are advised to cover on dips near 63.60 for near term," it said.
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The benchmark BSE Sensex ended higher by 200.34 points, or 0.74 per cent, at 27,316.17.
Meanwhile, RBI today fixed the reference rate of rupee at 63.8195 against the US dollar and at 72.3585 for the euro as against 63.8495 and 72.4564 yesterday.
The reference rate for Japanese yen was fixed at 51.8300 per 100 yen and 101.2560 for the pound.