The rupee ended the session weak at 64.08 as the dollar held steady in Tuesday's holiday-thinned trade, shrugging off upbeat Japanese economic data as market participants pondered about next year's potential catalysts.

The domestic unit opened strong by 2 paise at 64.02 at the Interbank Foreign Exchange market today. It hovered in a range of 64.11 and 64.02 before ending the session at 64.08, down 3 paise. On Friday, the rupee had ended flat at 64.05.

Meanwhile, the benchmark BSE index breached the 34,000-mark for the first time and ended higher by 70.31 points or 0.21 per cent at 34,010.61. The broader NSE index rose 38.5 points or 0.37 per cent to close at an all-time high of 10,531.50.

The euro inched down 0.1 per cent to $1.1869. The single currency gave up some ground last week after Catalan separatists won a regional election, deepening Spain's political crisis in a sharp rebuke to Prime Minister Mariano Rajoy and European Union leaders who backed him. Against the yen, the dollar was almost flat on the day at 113.30.

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