A cautious tone largely dominated forex trading amid heightened tensions in Korean peninsula.
The domestic currency was unable to gain any traction and continued to trade under pressure despite US dollar being weaker against key rivals overseas.
Heavy capital outflows also weighed on the rupee trade.
The rupee today opened on a weaker note at 64.10 against the dollar from Monday's close of 64.05 at the forex market on steady demand for the US currency.
The RBI, meanwhile, fixed the reference rate for the dollar at 64.1164 and for the euro at 76.2921.
The rupee has lost 22 paise in the last three sessions.
Meanwhile, local equities witnessed a smart recovery, notwithstanding global volatility shocks on the back of select buying in front-line counters even as cautious investors looked for bargains among beaten-down counters.
The flagship Sensex rose over 107 points to end at 31,809.55, while broader Nifty climbed 39 points to 9,952.20.
Asian markets were mostly lower as North Korea's nuclear programme loomed over trade.
Global currency and financial markets wobbled in knee- jerk reaction to North Korea's apparent test of a hydrogen bomb.
On the global front, the dollar was little changed against other major currencies, as investors remained cautious amid mounting tensions between the US and North Korea.
The dollar index, which measures the greenback's value against a basket of six major currencies, was down at 92.45.
In cross-currency trades, the rupee drifted further against the pound sterling to conclude at 83.09 from 82.93 per pound and also dropped against the Japanese yen to finish at 58.63 per 100 yens from 58.39.
In forward market today, premium for dollar lost further ground owing to consistent receivings from exporters.
The benchmark six-month premium payable in February moved down to 129-131 paise from 131.75-133.75 paise and the far forward August 2018 contract also slipped to 268-270 paise from 271.50-273.50 paise.
On the international energy front, crude prices staged a modest rebound on Tuesday following a gradual restart of Gulf of Mexico refineries after forced shutdowns due to Hurricane Harvey raised demand for crude.
Brent crude futures, the international benchmark for oil prices, dipped 13 cents to USD 52.21 a barrel in early Asian trade.
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