The Forex market was closed on December 25, for observing "Christmas".
Continued capital inflows too aided the rupee firm trend while USD demand from importers, mainly oil refiners, to meet their month-end requirements restricted the rise.
At the Interbank Foreign Exchange (Forex) market, the domestic unit commenced almost stable at 62.05 a dollar from last weekend's close of 62.04, but improved to log a two-week high of 61.78 on Tuesday.
Later, it dropped to a low of 62.17 on Thursday following strong dollar demand from importers and some banks before recovering to conclude the week at 61.85, revealing a gain of 19 paise or 0.31 pct.
The benchmark S&P BSE Sensex closed with week up by 113.86 points or 0.54 pct, while FIIs injected USD 157.01 mn during the first three trading days of the week.
Pramit Brahmbhatt, CEO of Alpari Financial Services (India) said, "Not much action was seen in the USD/INR pair last week, it traded range-bound for the week and closed better from previous week's close as US and Euro markets were closed due to Christmas."
"The rupee slightly appreciated to post its second weekly gain in a row. Immediate support for spot USD-INR pair is at 61.50. The trading range for the USD/INR is expected to be within 61.20 to 62.50," he said.
"With a relatively light economic calendar in the US and the Euro-zone owing to the holiday season, trading trends would be determined by the global factors," he added.
Forex dealers attributed steep fall in the rupee value on Thursday to strong dollar in the international market and high month-end demand from ONC and other importers.
In the absence of other prominent cues, the rupee mainly followed the equity markets and dollar inflow into Indian markets. FII's have build fresh positions in Indian equity markets after the expiry of the December series, aiding the rupee rally.
The rupee premium for the forward dollar ended mixed on alternate bouts of buying and selling.
The benchmark six-month forward dollar premium payable in May finished lower at 225-226 paise from last weekend's close of 229-1/2-231-1/2 paise, while far-forward contracts maturing in November moved up to 468-469-1/2 paise from 466-1/2-468- /2 paise.
The RBI fixed the reference rate for the US dollar at 62.0595 and for the euro to 85.2748 from 62.2420 and 84.8774 last weekend, respectively.
The rupee dropped further against the pound sterling to 102.15 from last weekend's close of 101.34 while fell back against the euro to 85.53 from preceding weekend's close 84.70.
However, it remained firm against the Japanese yen to 59.01 per 100 yen from previous weekend's close of 59.41.