The Japanese yen weakened 0.1 per cent to 109.65 per dollar, close to a seven-month low.
On a weekly basis, the rupee gained 86 paise or 1.19 per cent.
The local currency opened almost flat at 71.20 against the greenback.
The RBI bought $7.46 billion and sold $530 million in the market in November
The Kiwi dollar also edged up 0.2 per cent to $0.6622.
A strengthening domestic equity market supported the rupee, dealers said.
“Today, USDINR pair is expected to quote in the range of 71.50 and 72.05,” brokerage firm Motilal Oswal Financial Services said.
The dollar traded at 109.08 yen, jumping back sharply from a three-month low of 107.65 yen touched on Wednesday.
At the foreign bank exchange, the domestic unit opened significantly lower at 72.05 per dollar.
The local currency on Tuesday settled 11 paise up at to 71.82 against the greenback.
China's yuan held on to most of Tuesday's steep gains at 6.9460 per dollar, after a bumpy ride.
The rupee opened on a positive note at 71.73 against the US currency.
London has overtaken Mumbai to become the top center for trading the rupee
"USDINR pair is expected to quote in the range of 71.70 and 72.25,” said Motilal Oswal Financial Services.
Forex traders said growing geopolitical tensions could continue to keep the domestic unit under pressure.
The Japanese yen surged on Monday to a three-month high of 107.77 versus the US dollar.
The rupee lost about 0.60 per cent against the dollar in the first three trading sessions of 2020.
The dollar gained against riskier currencies such as the Aussie and the kiwi.
On Thursday, the domestic unit had dropped by 16 paise to end at 71.38 against the US dollar.
In the previous week, the reserves rose to $454.948 billion after increasing by $456 million.
Rupee is trading in a narrow range amid lack of directional cues from the global market.
The currency is set to extend losses as a truce in the US-China trade war and signs that global growth is improving sap demand for haven assets.
'The key risk is the BOC, which tends to talk more dovishly whenever CAD shows material strength'
The currency had closed the 2018 year at 69.77 to the US dollar.
The rupee on Monday appreciated by 4 paise to settle at 71.32.
Investors' appetite for risk helped drive the euro up 0.1 per cent to $1.1206.
During the day, the domestic unit saw a high of 71.30 and a low of 71.39.
Three-fourths of the participants expect the benchmark bond yield to rise to 6.75 per cent.
The rupee is the second worst performing Asian currency this year.
“Today, USDINR pair is expected to quote in the range of 71.40 and 71.90.”
The euro climbed as high as $1.1211, its strongest level since Aug. 13, in early Asian trading.
Rupee touched a high of 71.19 in morning trade but lost ground and fell to a low of 71.40.
During the day, the domestic unit fluctuated between a high of 71.22 and a low of 71.35.
Selling in domestic equities and a steady rise in crude oil prices weighed on rupee.
The offshore yuan strengthened slightly to 6.9905 yuan per dollar.
The domestic unit finally settled at 71.27, showing a fall of 9 paise over its previous close of 71.18.
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