Besides, the euro sank against the dollar to the lowest level in nearly nine years as investors worried about a possible Greek exit from the eurozone and sliding oil prices.
Traders said this also weakened the rupee sentiment amid sustained dollar demand from importers, including oil firms.
At the Interbank Foreign Exchange (Forex) market, the domestic unit commenced better at 63.37 a dollar from previous close of 63.41. It then improved further to a high of 63.30.
Later, the rupee met with strong resistance following crash in local stocks and hit a low of 63.62 before concluding at 63.57, a net fall of 16 paise or 0.25 per cent. This is its weakest close since 63.67 on December 29, 2014.
On Monday, the rupee lost 12 paise or 0.19 per cent.
In the Indian stock market, benchmark S&P BSE Sensex today plunged by 855 points, or 3.07 per cent, in its worst fall since July 6, 2009.
Meanwhile, the dollar index, a gauge of six major global rivals, was up by 0.25 per cent.
Veracity Group CEO Pramit Brahmbhatt said: "The Indian rupee depreciated almost by a quarter of a per cent, taking cues from dollar demand from oil companies. Local equities forced the currency to trade weak. The trading range for the spot rupee is expected to be within 63.20 to 64.00."
Oil prices continued to drop, with the US benchmark contract briefly falling below $50 a barrel for the first time in more than five years.
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