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This is the highest closing for the domestic currency since November 6.
Heavy selling in the greenback by exporters and banks as well as weakness in the dollar against other currencies overseas largely supported the rupee recovery.
The local currency also benefited from a strong rally in local equities.
Currency traders and exporters rushed to sell their receivables expecting a surge in dollar inflows from global investors in the face of Moody's decision to upgrade Indias sovereign rating after a gap of 14 years.
The sovereign rating upgrade comes close on the heels of a sharp improvement in country's ranking in the World Bank's ease of doing business survey.
Brent crude, the international benchmark, is trading a tad higher at $62.36 a barrel in early Asian trade.
Earlier at the Interbank Foreign Exchange (forex) market, the rupee opened higher at 65.08 against Monday's finish of 65.11 on bouts of dollar selling.
Maintaining a clear uptrend throughout the session, the home currency finally managed end at the day's highest level of 64.89, revealing a strong gain of 22 paise, or 34 per cent.
The rupee had settled 10 paise lower yesterday.
In cross-currency trades, the rupee bounced back against the pound sterling to settle at 85.90 from 86.30 per pound and also rebounded sharply against the Euro to close at 76.06 from 76.76.
The local unit continued its strong momentum against the Japanese yen to conclude at 57.66 per 100 yens from 58.06.
On the global front, the greenback held steady against other major currencies in cautious trade on Tuesday, amid ongoing political woes in Germany and uncertainty over a major tax reform plan in the US.
The dollar index, which measures the greenback's value against a basket of six major currencies, was up at 94.03 in early trade.
Elsewhere, the common currency euro is trading little changed against the US dollar after the roller-coaster ride on Monday caused by the collapse of coalition talks in Germany as Angela Merkel prefers new elections while German President Steinmeier looks for renewed discussions.
The British pound traded flat ahead of the senior government ministers' meeting over the Brexit bill and the Bank of England governor being grilled at the inflation report hearing in parliament.
In forward market today, premium for dollar remained sluggish due to persistent receiving from exporters.
The benchmark six-month premium payable in April moved down to 121-122 paise from 123-125 paise and the far forward October 2018 contract also eased to 261-262 paise from 262-264 paise yesterday.
On the international energy front, crude prices rebounded sharply as traders looked to a meeting next week at which major crude exporters are expected to extend production cuts, though rising US output capped gains.
Brent crude oil was up 47 cents at $62.69 a barrel, while US light crude was at $56.74, up 32 cents.
Analysts said Brent was expected to fluctuate in a narrow range, between $61 and $63, as the market awaited the outcome of the Organization of the Petroleum Exporting Countries' meeting this month.