However, consolidation in local equities and continued capital outflows capped the domestic currency's gains to some extent, forex dealers said.
The rupee commenced a tad higher at 54.80 from its previous closing of 54.81 on Friday at the Interbank Foreign Exchange (Forex) market.
It moved in a range of 54.54-54.84 before closing at 54.56, a rise of 25 paise, or 0.46 per cent.
Pramit Brahmbhatt, CEO, Alpari Financial Services (India) said: "Rupee continued to trade strong for the second day against the dollar taking cues from the euro, which traded strong against the dollar."
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The yen weakened beyond 99 against the dollar for the first time since May 2009 on hopes that Bank of Japan's recent measures to fight deflation will further weaken the currency.
"The Bank of Japan's plan for aggressive monetary easing was taken negatively by the investors, as a result yen traded weak and made new lows against major currencies," Brahmbhatt added.
Meanwhile, the BSE benchmark Sensex today closed down by a mere 12.45 points to 18,437.78, while foreign institutional investors sold local equities worth USD 37.24 million (Rs 203.18 crore), as per provisional BSE data.
"Going ahead in this week, we have a number of data in the form of inflation, IIP and trade figures, which will decide the further course of rupee," he added.