However, firm dollar overseas amid continued capital inflows restricted the rupee fall to some extent, a forex dealer said.
At the Interbank Foreign Exchange (Forex) market, the rupee commenced lower at 63.00 a dollar from last weekend's close of 62.47 and immediately touched a high of 62.93.
Later, it met with strong resistance and tumbled to a low of 63.91, two-month low, before recovering at the fag end to settle at 63.11, still showing a fall of 64 paise or 1.02 pct. In last five weeks, it has plunged by 208 paise or 3.39 pct.
The Indian benchmark Sensex tumbled by 266.73 points or 1.29 pct during the week while FIIs remained net buyers.
Widening of trade deficit from a month ago and strong US currency after encouraging jobs data renewed fears of stimulus tapering also weighed on the rupee.
Finance Minister P Chidambaram told reporters in New Delhi on Monday that the rupee will "settle down."
The Indian currency started declining as oil refiners resumed part of their dollar purchases from the market, Economic Affairs Secretary Arvind Mayaram had said.
"Rupee was seen depreciating against the US dollar due to persistent dollar strength, rising dollar demand from the domestic oil companies and debt market outflows. Also, the stock markets which ended the session on a negative note contributed to the weakness in the local currency," said Abhishek Goenka, CEO of India Forex Advisors.
Some recovery at the fag end was due to likely fresh sales of the US currency by exporters and by state-run banks on behalf of the RBI.
The Reserve Bank of India, seeking to calm the currency markets, Wednesday said the current account deficit in 2013-14 will be USD 56 billion, lower than earlier projections, and that there is no fundamental reason for rupee depreciation.
RBI Governor Raghuram Rajan said the central bank was weighing options to contain exchange rate volatility and would come out with 'appropriate' steps in the future.
RBI Governor sought to reassure investors, saying there is no fundamental reason for the currency to fall again. He also pegged the CAD at a lower level than estimated earlier.
Meanwhile, the inflation measured by the wholesale price index (WPI) rose to 7 pct in October compared with 6.46 pct in September.
The RBI said it would inject Rs 8,000 crore by purchasing bonds on Monday to improve liquidity in the system.
Mr. Pramit Brahmbhatt, CEO, Alpari Financial Services (India) said,"The Rupee continued to depreciate for the fifth consecutive week and traded nine-week low. Though, on friday Rupee continued its previous day strength and appreciated by over half percent during the day."
"Local equities closed up by over one percent, snapping a seven-session losing streak as lenders rallied after the central bank governor announced bond purchases, easing some concerns about losses in the sector tied to their heavy debt holdings, the central bank chief also clarified that the dollar demand from oil companies are smoothly absorbed by the forex market and easing fears of near-term tapering by the U.S. Federal Reserve which helped Rupee to trade positively for the day. The trading range for the USD/INR pair for the week is expected to be within 62.00 to 64.50."