Better dollar overseas also weighed on the rupee while sustained foreign funds inflow in record-breaking local equities restricted the rupee fall, a forex dealer said.
The forex market was closed on March 31 for "Gudi Padwa" and on April 1 for "annual closing of bank accounts".
At the Interbank Foreign Exchange (Forex) market, the domestic unit commenced strong at 59.80 a dollar from last weekend's close of 59.91 and improved further to a high of 59.50 -- a level not seen since July 29, 2013 when it had logged an intra-day high of 59.08 on firm local stocks.
It, later, moved in a wide range of 59.50 and 60.39 before settling the week at 60.08, showing a fall of 17 paise or 0.28 per cent. In last two-weeks, it had flared up by 128 paise or 2.09 per cent.
The benchmark S&P BSE Sensex came off from its new intra-day peak of 22,620.65, still closing the week up by near 20 points or 0.09 per cent while FIIs infused USD 815.36 million on the first four days of the week.
The Reserve Bank of India (RBI), at its April 1 policy meet, left the short-term lending rate, or repo, unchanged at 8 per cent and cash reserve ratio at 4 per cent. Brokers said the RBI's decision was largely in line with investor expectations and failed to have any major immediate effect on the market.