Weakness in the domestic stock markets also affected the rupee value against the dollar, a forex dealer said.
The rupee opened lower at 67.18 against yesterday's closing level of 67.14 per dollar at the Interbank Foreign Exchange market and hovered in a range of 67.09 and 67.30 before quoting at 67.27, showing a loss of 13 paise or 0.19 per cent.
The domestic currency has dropped by 62 paise or 0.93 per cent in four trading days.
The RBI fixed the reference rate for the dollar at 67.1520 and euro at 75.7542.
In cross-currency trades, the rupee firmed up further against the pound sterling to close at 95.22 from 95.24
on Monday and also moved up against the euro to 75.50 from 75.67 per euro previously.
However, the domestic currency dropped further against the Japanese yen to 63.49 per 100 yens from 63.33.
Meanwhile, the dollar index was up by 0.37 per cent against the basket of six global currencies in the late Asian trade.
Overseas, the US dollar gained against its major rivals in early Asian trade, while the British pound remained fragile near a two-month low against the dollar and the yen hovered near six-week highs against the US currency on worries Britain may leave the European Union in a referendum.
However, the yen gained moderately against the dollar and other currency peers in late Asian trade.
In forward market, premium for dollar inched up on mild paying pressure from corporates.
The benchmark six-month premium for November moved up to 194.5-196.5 paise from 194-196 paise previously and far forward May 2017 contract also looked up to 385.5-387.5 paise from 384-386 paise.
Pramit Brahmbhatt of Veracity Financial Services said, "The rupee opened on a positive note but later on taking cues from domestic equity market which was trading weak, the rupee too started depreciating since opening trades. Our benchmark index Nifty opened on a positive note but profit booking dragged it down to lower levels and closed with negligible loss of 2 points at 8,109 levels."
Thus to end the day, the rupee closed at 67.27/USD against the previous close of 67.14/USD thus by depreciating 13 paise.
Trading range for the spot USD/INR pair will be 67 to 67.50/USD.
Meanwhile, oil prices fell more than 1 per cent in Asia today, extending a sell-off on speculation about a pick-up in production while world markets are rattled by fears over Britain's possible exit from the European Union.
US benchmark West Texas Intermediate fell 56 cents, or 1.15 per cent, to $48.32 and Brent slipped 51 cents, or 1.01 per cent, to $49.84.
Meanwhile, the benchmark Sensex ended slightly lower by 1.06 points to 26,395.71.
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