The domestic currency resumed slightly higher at 66.63 against last Wednesday's level of 66.65 a dollar at the interbank foreign exchange (Forex) market and hovered in a range of 66.5225 and 66.7100 before finishing at 66.55, showing a gain of 10 paise.
The dollar index was down 0.12 per cent against a basket of six global currencies in the late afternoon trade.
The dollar was sharply lower against rival currencies on Monday after major oil producers failed to reach a deal to curb production, prompting investors to rush into the safe-haven Japanese currency.
Meanwhile, the Reserve Bank of India (RBI) fixed the reference rate for the dollar at 66.6663 and euro at 75.2596.
In cross-currency trades, the rupee advanced further against the pound sterling to close at 94.33 from 94.86 last Wednesday.
It also moved up further against the euro to 75.26 per euro from 75.32 while declined against the yen to 61.49 per 100 yens from 60.96 previously.
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