Besides, lower dollar in the overseas market affected the market sentiment.
The rupee resumed higher at 63.95 as against yesterday's closing level of 64.12 at the Interbank Foreign Exchange (Forex) and firmed up further to 63.70 before concluding at more than 2-week high at 63.73, a gain of 39 paise, or 0.61 per cent.
The local currency has gained 53 paise, or 0.82 per cent, in two days.
The dollar extended its losses against the yen and the euro in Asian trade today after a lack of clear commitment by the Federal Reserve to raise interest rates in September indicated continued caution at the US central bank.
In New York market, the dollar weakened against the yen and euro yesterday after Federal Reserve policy makers indicated in their latest policy statement that the pace of interest-rate hikes might be slower than previously expected.
Meanwhile, the benchmark BSE Sensex ended higher by 283.17 points, or 1.06 per cent, at 27,115.83.
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